Dr Jonathan De Roo
email: jonathan.deroo@ugent.be

Edwin A Baquero

# Yannick Coppel

Katrien De Keukeleere

Isabel Van Driessche

Céline Nayral

Zeger Hens

Fabien Delpech
email: fdelpech@insa-toulouse.fr

# Both

Prof. dr Fabien Delpech

Insights in the ligand shell, the coordination mode and reactivity of carboxylic acid capped metal oxide nanocrystals

Keywords: carboxylates, nanocatalysis, nanoparticles, NMR, surface chemistry

A detailed knowledge of surface chemistry is necessary to bridge the gap between nanocrystal synthesis and applications. Although it was proposed that carboxylic acids bind to metal oxides in a dissociative NC(X)2 binding motif, this surface chemistry was inferred from indirect evidence on HfO2 nanocrystals (NCs). Here, we show a more detailed picture of the coordination mode of carboxylate ligands on HfO2 and ZrO2 NC surfaces, by direct observation via solid state NMR techniques. Surface adsorbed protons are clearly distinguished and two coordination modes of the carboxylic acid are noted; chelating and bridging. We also find that secondary ligands penetrate the ligand shell and have the same orientation with respect to the surface as the primary ligands, indicating that the ionic or hydrogen bond interactions with the surface are more important than the van der Waals interactions with neighboring ligands. During ligand exchange with amines, the chelating carboxylate is preferentially removed. Finally, we show that the HfO2 and ZrO2 NCs catalyze the imine formation from acetone and oleylamine. Together with the already reported catalytic activity of hafnium oxide, these results put colloidal metal oxide nanocrystals squarely in the focus of catalysis research.

Introduction

Colloidal nanocrystals (NCs) have been synthesized in various sizes, compositions and shapes, [1] all sharing the same fundamental characteristic: a large surface area. The surface can be either manipulated, used or passivated but cannot be neglected for most applications such as catalysis, [2] thermoelectrics, [3] nanocomposites, [4] thin film electronics, [5] optoelectronics [6] or electrochromic devices. [7] The NC surface determines the colloidal stability and the physico-chemical properties of the NCs. For these reasons, the surface is often capped with organic surfactants, hence the identification of a colloidal NC as a hybrid object with an organic-inorganic interface. Characterizing the NC core-ligand interface (i.e., the binding modes, the dynamics and the reactivity of the ligands) demands analytical tools probing the NC surface at the molecular scale. Among the various surface characterization methods such as infrared (IR) and X-ray photoelectron spectroscopy (XPS), nuclear magnetic resonance (NMR) stands out due to its high resolving power. [8] Combining solution 1 H NMR and elemental analysis (inductively coupled plasma -mass spectroscopy, ICP-MS), it was established that binary metal chalcogenide nanocrystals such as PbSe and CdSe NCs are cation rich and the charge is balanced by X-type carboxylates in a binding motif denoted as NC(MX2), see Scheme 1. [9] Furthermore, this MX2 unit as a whole, is a Z-type ligand and can also be involved in ligand displacement, having a great impact on the optical properties of the nanocrystals. [6d] In contrast, carboxylic acids are able to dissociate on stoichiometric metal oxide NCs. [10] Presumably, protons bind to surface oxygen atoms whereas carboxylates bind to surface metal sites, a binding motif denoted as NC(X)2, see Scheme 1. This combination of X-type ligands is charge neutral as a whole, and allows for ligand displacement by L-type amine ligands. [11] Furthermore, the surface protons were shown to greatly affect the redox chemistry of ZnO nanocrystals [12] and determined the catalytic activity of HfO2 NCs. [2a] Another example of the NC(X)2 motif is found in case of stoichiometric CsPbBr3 perovskite NCs, which are dynamically stabilized by an ion pair: alkylammonium carboxylate (Scheme 1). [13] The deep understanding of NC surface chemistry has led to a rationalization of ligand exchange and has been advancing NC applications. [14] Further elaboration on the LXZ classification, binding motifs and ligand exchange can be found elsewhere. [2a, 14] Scheme 1. The surface chemistry of NCs, stabilized by carboxylates/carboxylic acids.

Unfortunately, the surface chemistry was often inferred indirectly since proton or carbon nuclei close to or on the surface are not detectable in solution 1 H NMR. [15] Although derivatization and ligand exchange are commonly used to characterize ligands, [10,16] they are invasive, ligand-specific processes that may have uncontrolled effects such as surface oxidation or residual water adsorption. [16c] Furthermore, solution 1 H NMR does not allow to determine relations between different ligands and different surface sites (as is the case in the NC(X)2 motif). On the other hand, solid state NMR (ssNMR), especially using the crosspolarization (CP) sequence, is of high relevance in the context of surface characterization and mobility-restricted fragments or ligands: the low motion can be advantageously used through the CP experiment to enhance the signals which are typically too broad and too weak to be observed. This is usually achieved using traditional 1D 1 H-X CP (X= 13 C, 31 P, 77 Se…) or 2D 1 H-X heteronuclear correlation (HETCOR).

In this paper, we study two technologically relevant metal oxide NCs; hafnium and zirconium oxide for their use in photoluminescence, [17] catalysis, [2a] volume holography, [4d] biomedical applications, [18] superconducting nanocomposites, [4b] γ-ray scintillators [4c] and high κ or high refractive index nanocomposites. [19] We use solid state NMR to shed light on the nature of interaction between the NC surface and both primary and secondary ligands. A first group of ligands is covalently interacting with the surface and a second group of ligands is hydrogen bonding or electrostatically interacting. In addition, we confirmed the NC(X)2 binding motif that was inferred from solution NMR measurements. [10][11] It is shown that both on ZrO2 and HfO2 NCs, carboxylates have two different coordination modes (chelating and bridging) whereas the bridging mode is clearly favored. We show unambiguously the presence of surface protons and their correlation with the bridging carboxylate mode, uncovering an unprecedented level of detail compared to previous ssNMR studies of carboxylic acid capped ZrO2 and HfO2 particles. [20] After ligand exchange with L-type amine ligands and purification with acetone, the chelating mode is removed and in the supernatant, an imine product is found, indicating a catalytic effect whereas the extent of imine formation is higher for HfO2 NCs.

Results and Discussion

Nanocrystal synthesis and solution NMR. Aggregated, HCl capped ZrO2 and HfO2 NCs were synthesized in benzyl alcohol from the respective metal chloride precursor. [21] As expected, the monoclinic crystal phase is recognized in the XRD diffractogram of both ZrO2 and HfO2 (Figure S1). The NCs were de-aggregated by a post-synthetic surface modification [4d, 10, 21b, 22] with dodecanoic acid and oleylamine (Scheme 2). It was earlier inferred from solution 1 H NMR experiments [10, 21b] that dodecanoic acid is the primary ligand, tightly bound to the NCs in a monolayer. Oleylammonium chloride and excess dodecanoic acid are secondary ligands, interacting weakly with the surface, a state which was vaguely described as "entangled" in the ligand shell or physisorbed. [10,23] These secondary ligands could be removed by extensive purification (Scheme 2). The HfO2 NCs are about 5 nm and slightly ellipsoidal while the ZrO2 NCs are more irregularly shaped but also around 5 nm in size (Figure 1A and1B). Thoroughly purified NCs feature only broadened resonances in the 1 H NMR spectrum (Figure 1C), pertaining to a monolayer of tightly bound dodecanoic acid. The resonances of oleylammonium chloride are absent. It is clear that no additional information about the coordination of dodecanoic acid to the surface can be extracted from the spectrum since resonances 1 and 2 are simply not observed. This finding is not unexpected since tightly bound surfactants have a significantly reduced mobilityinducing line broadening in NMRand this effect is more predominant the closer protons are located to the surface. Therefore, the first CH2 units next to a functional group (e.g., carboxylic acid) are broadened beyond detection and small ligands are even completely invisible in solution 1 H NMR. [15] ZrO2 -ligand shell configuration. To obtain a more complete picture on the ligand shell, we turned to solid state NMR. Two ZrO2 NC samples were prepared, either purified five times (5x) by precipitation with acetone or only once purified (1x). In solid state 13 C direct polarization (DP) MAS, all the carbon resonances are probed. Indeed, the carbonyl (181.6 ppm) and αCH2 (37.2 ppm) resonances of dodecanoic acid are observed in the DP MAS spectrum of 5x purified ZrO2 NCs (Figure 2). The alkene resonance is not observed, confirming the absence of oleylammonium chloride in the ligand shell. To increase the signal to noise ratio, and to assess the ligand orientation on the surface, cross polarization (CP) is used. As the gyromagnetic ratio of 1 H is four times higher than of 13 C, a magnetization transfer of protons to carbons results in 13 C signal enhancement. Interestingly, the enhancement is more efficient in case of restricted mobility, rendering CP ideal to study ligands attached to NC surfaces. [24] The transfer of polarization takes place at the millisecond time scale so for nuclei with mobility faster than milliseconds, the transfer of polarization (and thus signal enhancement) will not be effective. [25] Therefore, the 13 In the spectra of the 1x purified ZrO2 NCs (Figure 2), there is an additional resonance at 129.2 ppm pertaining to the carbon-carbon double bond of the oleylamino fragment. This indicates that purifying once is not enough to remove the oleylammonium chloride. Most interestingly the αCH2 resonances of both oleylammonium chloride and dodecanoic acid (tightly bound and excess) are not detected in the INEPT experiment, indicating that all αCH2 resonances are close to the surface. This proves that the orientation of the secondary surfactants is the same as the orientation of the tightly bound dodecanoic acid; the hydrophilic head towards the surface. This sheds light on the vague term 'entanglement' which was used to described the weakly bound state of surfactants. [10] Since random van der Waals interactions would lead to a random orientation in the ligand shell, we conclude that the second coordination layer is interacting through hydrogen bonds or electrostatic interaction with the polar surface or the polar functional group of the tightly bound surfactants.

ZrO2 -ligand binding modes. In the 1 H-13 C CP MAS spectra of both 1x and 5x purified ZrO2 NCs, the carbonyl region features two signals (at 189.3 and 181.6 ppm), probably related to two different coordination modes. It is surprising that both modes survived the washing procedure, indicating a strong interaction with the NC surface. Thanks to the frequency difference between the antisymmetric and symmetric ν(CO2 -) stretches (130 cm -1 , see Figure S2), ionic and monodentate bonding modes can be ruled out since this would require a frequency difference of at least 160 cm -1 . [START_REF] Nakamoto | Infrared and Raman Spectra of Inorganic and Coordination Compounds[END_REF] However, it is sometimes misleading to discriminate the two other potential bonding modes (chelating bidentate and bridging bidentate) only via IR data. [START_REF] Ye | [END_REF] Fortunately, the carbonyl 13 C NMR chemical shift of carboxylate ligands has been shown to be a highly sensitive probe to diagnose with high resolution the binding modes of the carboxylate. [START_REF] Ye | [END_REF] The well-documented chemistry of zirconium carboxylates features polynuclear structures, in which the carboxylate ligands can display either a chelating coordination mode or a bridging bidentate one. Both ligation modes are straightforwardly identified in view of the significant difference of the chemical shifts, the chelating mode being shifted 5 to 13 ppm downfield. [28] This shift is in line with previous work on zinc carboxylate where this was explained by electronic effects of the bound metal. [START_REF] Ye | [END_REF] It is thus reasonable to assign the resonances at 189.3 and 181.6 ppm respectively to chelating and bridging coordination modes. In the 1 H MAS spectrum of the 5x purified NCs (Figure 3A), a broad contribution was identified next to the expected resonances of dodecanoic acid. We attribute this broad resonance (in green) to protons on the ZrO2 NC surface, denoted as Zr-OH. Importantly, the carbon resonance at 181.6 ppm shows a correlation with the Zr-OH (Figure 3B), indicating the proximity of zirconol moieties to the carboxylate. Based on these observations, we depict the coordination modes in scheme 3. The 189.3 carbonyl resonance corresponds to a chelating binding mode and the interpretation is straightforward. The most likely coordination for the bridging mode (181.6 ppm) is the situation where a carboxylate bridges a hydrogen and a zirconium atom (Scheme 3A). This satisfies the requirement for bridging coordination and takes into account the correlation to Zr-OH. However, on the basis of these data the presence of a carboxylate bridging two zirconium atoms, cannot be fully discarded (Scheme 3B).

Nevertheless, in this case, a random position of the zirconol at the surface is expected and thus, some interactions (and the subsequent correlation in the HETCOR spectrum) should also be observed with the chelating carboxylates. The most exiting result is that the prevalent bridging coordination seems to confirm the surface chemistry binding motif NC(X)2 where two X-type moieties (proton and carboxylate) are interacting with two different surface sites (zirconium and oxygen). However, it should be noted that the present experiments also indicate that there is still a proton-carboxylate interaction and that the carboxylic acid is thus not completely dissociated. In this respect, one may argue that carboxylic acids can be regarded, not as a combination of 2 X-type ligands but rather one ligand with two X-type functionalities; NC(X2) instead of NC(X)2. Generalization to HfO2 NCs. The same experiments were conducted for HfO2 NCs. About the same frequency difference (136 cm -1 ) was found between the symmetric and the antisymmetric carbonyl stretch in the IR spectrum (Figure S3). Indeed, the coordination modes of dodecanoic acid towards the hafnia surface are identical as to the zirconia surface since the same carbonyl resonances are apparent from the CP MAS spectrum (Figure 4A). The αCH2 resonance is again not detected in the INEPT experiment, confirming the orientation of dodecanoic acid to HfO2. The surface hydroxyl groups are clearly detected in the 1 H MAS spectrum (Figure 4B) and the correlation with the bridging mode is apparent from the HETCOR experiment (Figure 4C). Although HETCOR is powerful, the experiment is also time consuming. Recently, Delpech and coworkers have proposed the use of a Forth and Back CP experiment (FBCP) where polarization is transferred from hydrogen to phosphorus atoms of a NC and back to hydrogen atoms. [29] In this way, it was possible to selectively probe the hydrogen atoms on and close to the phosphorus atom at the NC surface. In our case of HfO2 NCs, the inorganic core does not contain any abundant NMR sensitive nucleus, hampering the technique. However, the carbonyl carbon is quite isolated in the 13 C NMR spectrum and therefore, it was possible with the use of selective pulses to edit hydrogen atoms close to carbonyl through selective polarization transfers. The surface hydroxyl groups are now clearly apparent in the 1 H FBCP NMR spectrum (Figure 4B). Ligand exchange. It is known from literature that amine ligands are able to displace carboxylic acids on metal oxide surfaces when provided in a large excess. [11] To investigate the influence of this ligand exchange to the coordination modes, we added 10 equivalents of oleylamine to the 5x purified ZrO2 and HfO2 NCs, dispersed in chloroform. This causes the displacement of 13 % of the original carboxylate capping layer (Figure S4). We subsequently purified the dispersion three times with acetone and investigated the resulting NC powder and the first supernatant. Although the IR spectra before and after amine treatment look identical (Figures S5 andS6), the ssNMR spectra are more revealing. It appears that the chelating mode has vanished in the case of ZrO2 NCs and decreased considerably in intensity in the case of HfO2 NCs (see Figure 5). These results clearly show a higher reactivity of the carboxylate ligand in chelating mode than that one in bridging mode towards the ligand exchange by oleylamine. This selectivity in the reaction can be explained by the higher electrophilicity of the carboxylate moiety in the former mode compared to the latter. The different electrophilicity of these carboxylates is also supported by the difference in their chemical shift of the 13 C carboxylate nuclei (189.3 vs. 181.6 ppm for chelating and bridging mode, respectively vide supra). This is attributed to electronic effects of the bound metal. [START_REF] Ye | [END_REF] Nanocatalysis. Analysis of the supernatant revealed the formation of an imine product (see Figure 6). This is derived from the condensation reaction between oleylamine and acetone; the solvent used for the precipitation of both ZrO2 and HfO2 NCs. The characterization of the imine is available in the supporting info (Figure S7). A higher imine content was found in the supernatant of the HfO2 NCs as determined by solution 1 H NMR spectroscopy (95% vs. 75% for HfO2 and ZrO2 respectively). The conversion yield was calculated based on oleylamine. In order to confirm the nature of the reaction (NC-catalyzed or stoichiometric), a control experiment between oleylamine and acetone was performed, in the presence or absence of dodecanoic acid. Under the same conditions as the nano-catalysis (40 min at room temperature, [oleylamine] = 0.076 M and [acetone] = 10 M), the reaction only proceeded 13 or 14 %, with or without dodecanoic acid respectively ([dodecanoic acid]=0.0076 M), on the basis of 1 H NMR spectroscopy. This result confirms that ZrO2 and HfO2 NCs are acting as nano-catalysts in the condensation reaction, as it is well known that the synthesis of imines from carbonyl compounds can be acid-catalyzed. [30] The control experiment with dodecanoic acid suggests that the reaction might be more likely catalyzed by the Lewis acid (hafnium or zirconium) surface sites rather than by the Brønsted acidity of adsorbed carboxylic acids, although the influence of hydrogen bonding cannot be excluded. Imines are important intermediates in the synthesis of various biological, agricultural, and pharmaceutical compounds since they can undergo versatile transformations (reductions, additions, condensations, and multicomponent reactions. [30][31] The high conversion percentage at room temperature, especially for HfO2, shows the potential of these metal oxides as nanocatalysts for this reaction. Although it should be noted that imines can be produced from alcohols and amines by using Pd or Au on a zirconia support, [32] this is the first example (to the best of our knowledge) in which ZrO2 or HfO2 serve as the sole nano-catalyst for imine formation. Together with the recently discovered catalytic activity of HfO2 in the esterification and transesterification reaction, [2a] these results put zirconia and hafnia squarely in the focus of acid-base catalysis and further optimization is required to bring these materials to their full potential.

Conclusion

Solid state NMR analysis was able to reveal unprecedented details on ligand shell configurations. We contributed to the discussion on secondary "entangled" ligands and show that those ligands are interacting with the surface through hydrogen bonding and electrostatic interaction. We also confirm the NC(X)2 binding motif of carboxylic acids on ZrO2 and HfO2 NC surfaces. Through the application of HETCOR and FBCP, the surface protons were identified and correlated to the carbonyl carbon of a carboxylate in a bridging coordination mode. Also a minor chelating mode was identified. During ligand exchange with oleylamine, the chelating mode appeared to be more reactive and was readily displaced. We also found that the zirconia and especially the hafnia NCs catalyzed the imine formation of acetone with oleylamine. These results confirm the importance of zirconia and hafnia for catalysis and widen the scope of their catalytic applications.

Experimental section

Nanocrystal synthesis. HfO2 and ZrO2 NCs were synthesized via an established microwaveassisted solvothermal process. [10, 21b] The precursor preparation was executed in a nitrogen filled glovebox. Very briefly, 0.5 mL of dibenzyl ether was added to 0.56 mmol (0.13 g) of ZrCl4, after which 4 mL of benzyl alcohol is added. After microwave heating at 210 °C for 3.5 hours, diethyl ether is added, causing phase separation. The particles are precipitated with ethanol and diethyl ether and washed once with diethyl ether. Finally the particles are redispersed in chloroform by the addition of 50 µL oleic acid and 50 µL oleylamine and ultrasonic treatment. The particles are purified five times with acetone. A more detailed description of synthesis procedure and work-up can be found elsewhere. [10] Solution NMR Characterization. 1 H-, 13 C-, COSY, HSQC, and 1 H-13 C HMBC-NMR spectra in solution were recorded on a Bruker Avance 500 NMR spectrometer. Chemical shifts (δ, parts per million) are quoted relative to SiMe4 ( 1 H, 13 C). They were measured by internal referencing to the 13 C or residual 1 H resonances of the deuterated solvent (CDCl3 1 H δ 7.26; 13 C δ 77.2; respectively). Coupling constants (J) are given in Hertz.

Solid State NMR Characterization. Solid-state NMR experiments were recorded on a Bruker Avance III spectrometers operating at magnetic fields of 9.4 T. Samples were packed into 3.2mm zirconia rotors. The rotors were spun at 16 kHz at room temperature. For 1 H MAS and 13 C DP MAS experiments, small flip angle (~30°) were used with recycle delays of 5 s and 10 s respectively. 13 C CP MAS were recorded with a recycle delay of 2 s and contact times between 2 ms and 5 ms. 13 C INEPT were recorded with a recycle delay of 3 s. The 13 C HETCOR were acquired with a contact time of 3 ms and a recycle delay of 1.5s. The Forth and Back CP (FBCP) experiment were conducted with a recycle delay of 1.5 s, a first contact time (forth, 1 H -> 13 C) and a second CP contact (back, 13 C -> 1 H) of 0.5 ms. Residual 1 H signals were eliminated with a saturation protocol that uses a loop of π/2 pulses with a timedecreasing interval (from 100 ms to 10 ms by steps of 10 ms). Carbonyl resonance were selected by replacing in the FBCP experiment, the second 90 degree hard pulse of 13 C by a 90 selective Gaussian shape pulse of 300 μs length. Chemical shifts were referenced to liquid TMS.

Other Characterization. FT-IR spectra were recorded on a Perkin-Elmer Spectrum 100 FT-IR spectrometer (solid state samples). For X-ray diffraction (XRD) characterization a Thermo Scientific ARL X'tra X-ray diffractometer was used with the CuKα line as the primary source.

Transmission electron microscopy (TEM) images were taken on a JEOL JEM-2200FS TEM with Cs corrector.

TOC entry TOC text

Solid state NMR showed that entangled carboxylic acid ligands are interacting with the nanocrystal surface through hydrogen bonding and electrostatic interaction. Tightly bound carboxylic acids are mostly adsorbed on the NC surface with both proton and carboxylate. Also a minor chelating mode was identified.

Scheme 2 .

 2 Scheme 2. Surface modification and purification of ZrO2 and HfO2 NCs.

Figure 1 .

 1 Figure 1. (A) TEM pictures and derived histograms of HfO2 NCs and (B) ZrO2 NCs. (C) Solution 1 H NMR spectrum of a NC dispersion stabilized by dodecanoic acid and purified 5 times with acetone. The resonance denoted by * is attributed to acetone.

  C signal intensities obtained with different polarization transfer schemes, CP, DP and INEPT (Insensitive Nuclei Enhanced by Polarization Transfer) yield information on molecular dynamics. DP yields quantitative spectra of all 13 C nuclei in the sample, while CP and INEPT select molecular segments being rigid (with order parameter S > 0.5 and/or rotational correlation time τc > 10μs) or mobile (S < 0.05 and τc < 0.01μs), respectively. Comparing the CP and DP MAS spectrum of 5x purified ZrO2 NCs (Figure 2), we observe a decrease in intensity of the CH3 resonance (13.5 ppm), relative to the αCH2 resonance. On the other hand, in the INEPT MAS spectrum, the αCH2 resonance is absent and the CH3 is the most intense resonance. Since the INEPT experiment probes the part of the sample with mobility, the CP and INEPT experiment both indicate a high mobility for the CH3 and a low mobility for the αCH2. Therefore, the carboxylate functional group is interacting with the surface and the methyl group is much further away from the surface.

Figure 2 .

 2 Figure 2. INEPT MAS, 1 H-13 C CP MAS and 13 C DP MAS spectrum of dodecanoic acid capped ZrO2 NCs purified once or five times.

Figure 3 .

 3 Figure 3. (A) 1 H MAS spectrum and (B) 13 C-1 H HETCOR of ZrO2 NCs purified five times.

Scheme 3 .

 3 Scheme 3. The three possible binding modes on the surface of ZrO2 NCs.

Figure 4 .

 4 Figure 4. (A) 13 C DP, 1 H-13 C CP and INEPT MAS spectra and (B) 1 H MAS and 1 H-13 C-1 H FBCP MAS spectra and (C) HETCOR spectrum of 5x purified HfO2 NCs capped with dodecanoic acid.

Figure 5 .

 5 Figure 5. 13 C CP MAS spectra of ZrO2 and HfO2 NCs before and after addition of oleylamine and purification.

Figure 6 .

 6 Figure 6. Solution 1 H NMR spectrum of the supernatant after purification of oleylamine treated ZrO2 NCs with acetone, showing imine formation between acetone and oleylamine.

Acknowledgements

This work was financially supported by the Research Foundation Flanders (FWO) and by the Agence Nationale pour la Recherche (Project ANR-13-IS10-0004-01). EAB is grateful to Marie Curie Actions and Campus France for a PRESTIGE post-doc fellowship (FP7/2007-2013) under REA grant agreement n° PCOFUND-GA-2013-609102.

Author contributions

JDR synthesized the NCs and wrote the manuscript. YC carried out the NMR measurements.

EAB carried out the IR measurements and wrote the manuscript. KDK performed TEM measurements. FD, CN supervised the research in Toulouse and FD wrote the manuscript.

IVD and ZH supervised the research in Ghent. All authors analyzed the results and commented on the manuscript.

Competing financial interests

The authors declare no competing financial interests.


Ferdaouss Mattoussi
email: ferdaouss.mattoussi@insa-rennes.fr

Matthieu Crussière
email: matthieu.crussiere@insa-rennes.fr

Jean-Franc ¸ois Hélard
email: jean-francois.helard@insa-rennes.fr

Gheorghe Zaharia
email: gheorghe.zaharia@insa-rennes.fr

Analysis of Coding Strategies within File Delivery Protocol Framework for HbbTV based Push-VoD Services over DVB Networks

Keywords: HbbTV, Push-VoD services, AL-FEC, repetition code, Markov chain, DVB

Hybrid broadcast broadband TV (HbbTV) is a technique providing Push-VoD services over an interactive hybrid TV. These services are broadcast using File Delivery Protocol (FDP) which includes different coding strategies to ensure a reliable delivery. This protocol is characterized by three levels of data representation giving rise to segmentation of packet losses which may result in poor recovery capabilities. This paper provides a first thorough investigation of coding FDP framework for a reliable delivery of Push-VoD service over DVB networks. We propose Markov modeling for characterizing inter-layers loss propagation within FDP on a wide variety of burst erasure channels. Based on this analytical analysis and a simulation study, we determine the possible recovering areas and the accurate loss measurements within FDP. The latter are then used to effectively investigate and configure the different coding strategies provided within FDP. In addition, we present a suitable recovering strategy for FDP which guarantees transmission robustness against the broadcast network impairments.

I. INTRODUCTION

A. The context of non-linear data transmission using HbbTV

The Television (TV) is probably the most cost-effective platform for informing, educating and entertaining people over the world. From the late 19 th century, the invention of the television was the work of many individuals and corporations in various parts of the world to deliver a device that supersedes previous technology and fills the people requirements. This induces the transition from black-and-white TV to the Digital TV (DTV) with high definition (HD) screens. The launch of the DTV and the big growth of the internet, becoming present to everywhere and everybody, have allowed the wealth of audio-visual experiences and the opportunity for apparition of the interactive TVs (iTV)s. Connected TVs, known nowadays by SmartTV or NetTV, represent a category of iTVs capable of displaying, separately, both TV programs from a broadcasting network and additional services delivered via an Internet connection (e.g. catch-up TV services). The separation between these services and linear broadcast TV services makes the surfing between the two worlds inflexible and inappropriate. In order to cope with these inconveniences, many broadcasters are advocating solutions that seek to combine the functionalities of both broadcast and broadband tuners in a device to offer interactive applications with a seamless experience to the consumer. Several approaches have been proposed, in different countries, to achieve this requirement yielding an optimum experience (greatly enhance the viewing experience) such as DVB Globally Executable MHP (GEM) in Italy [1], Youview in UK, and Hybrid broadcast broadband TV (HbbTV) in Germany, France and elsewhere [START_REF][END_REF].

HbbTV technology was developed by the HbbTV group including both television broadcasters and CE companies and standardized by ETSI as a norm (ETSI TS 102 796) [START_REF][END_REF]. This technology is a pan-European initiative aiming at harmonizing video broadcast and high-speed transmission standards to entertainment programs broadcast on connected TVs, set-top-boxes (STB) and multi-screen viewing devices. HbbTV provides viewers a richer experience of enhanced and interactive hybrid TV, through the provision of innovative services on both broadcast and broadband networks, allowing the viewer to interact with the current TV program. More precisely, with such a system, "red button" services linked to TV programs is implemented to provide interactive applications in a much more functional and flexible way. In addition, HTML overlays are possible on full-screen TV pictures as well as the integration of a scaled TV image into a full-screen application: obtain real "hybrid" approach to "connected TVs". Generally, there are two types of applications when referring to HbbTV; bound application or "broadcast-related" and unbound application or "broadcast-independent". The broadcast-related applications are tied to a current broadcast service (e.g., vote, quiz) whereas the broadcast-independent applications have no relation to any broadcast service and are accessible through a portal delivered by TV manufacturers (e.g., electronic program guides (EPGs), YouTube). HbbTV represents a more specific profile of available tech-A c c e p t e d m a n u s c r i p t nologies than a completely new technical development. It introduces only few new technical components. It is mainly based on DVB, CE-HTML and Open IPTV Forum (OIPF)s browser profile standards. The two latter standards define the main functionality of the HbbTV browser running on a TV, combining the TV picture with HTML pages [3]. DVB standard specifies and grants more DVB-related integration capability that is required to signaling and carriage of the interactive applications (HbbTV applications) in the hybrid environments [4]. HbbTV combines data and applications received via the broadcast signal with services, applications and contents provided via the Internet. HbbTV applications are signaled in Application Information Table (AIT) in Program Specific Information/Service Information (PSI/SI) tables. Depending on the HbbTV application type, it is possible to deliver HbbTV applications in two ways [START_REF][END_REF]:

• The first consists in encapsulating application data into Digital Storage Media -Command and Control (DSM-CC) 1 object carousels and sending it by broadcast channel. The application, which is fragmented (into separate files or into separate updates to files or trees), can be delivered synchronously with the program signal and presented progressively to the user with a different carousel period, depending on the nature and importance of each fragment. This allows time accurate data such as questions or answers for an interactive quiz show to be conveyed. This protocol is specified to transfer application data 2 and stream events (data streams) [4]. • The second way consists in signaling application as a link to remote HTTP server over broadcast channel in AIT in PSI/SI tables and download applications over broadband channel. The data from both delivery channels are processed seamlessly in one application.

Since the appearance of HbbTV, several releases have been made proposing and/or adding services, features and enhancements. For instance, the most important advancement of HbbTV v2.0 version standardized in May 2015, was the integration of selections from HTML 5 and other next generation web technologies, the support of second-screen devices allowing a platform-independent user experience, as well as the addition of the Push-VoD service [START_REF][END_REF]. The present paper focuses on this release and more precisely on the Push-VoD service.

B. Reliability of unidirectional content delivery

One of the main requirements of the file broadcast service is the reliable delivery, which means efficiently dealing with the problems caused by erasure-prone broadcast networks. Over broadcast networks, both the absence of any return channel and the unlimited scalability in terms of number of receivers who behave in a completely asynchronous way, prevent the use of repeat request mechanism to adapt and individualize transmission rates according to some feedbacks sent by receivers. Therefore, content broadcasting heavily relies on Forward Erasure Correction (FEC) mechanisms to improve transmission robustness against channel erasures. The great advantage of using FEC with broadcast transmissions is that the same repair packet can recover different lost packets at different receivers. In that perspective, upper layer FEC mechanisms can be very beneficial for file delivery/download services in unidirectional multicast/broadcast environments. It shortens the transmission duration and reduces bandwidth requirements while ensuring that the receivers reliably obtain the file. Application-Level FEC (AL-FEC) code, which is partially integrated in the application layer above the IP level, has become a key component of many content delivery systems. It is widely used as an efficient technique to increase the native reliability of the network to meet the requirements of the content download/delivery services through the recovery of packets lost in transmission, as it can decrease download times as well as network traffic, since it avoids the request of lost packets [6]. There are many studies concerning reliable file content delivery over unidirectional packet erasure channels. For instance, to increase the robustness of DVB-H file delivery in IP Datacast Content Delivery Protocol (IPDC CDP), a systematic Raptor AL-FEC code was adopted with the File Delivery over Unidirectional Transport (FLUTE) 3protocol for use instead of the MPE-FEC of the link layer [START_REF]Digital video broadcasting (DVB); IP datacast over DVB-H: Content delivery protocols[END_REF]. Similar to the DVB-H, the same Raptor AL-FEC code with FLUTE protocol was used in IPDC CDP for DVB-SH file delivery [START_REF]Digital video broadcasting (DVB); IP datacast: Content delivery protocols (CDP) implementation guidelines; part 2: IP datacast over DVB-SH[END_REF]. In DVB-IPTV Content Download Services (CDS), the same AL-FEC based Raptor code of the IPDC CDP file delivery over DVB-H and DVB-SH was selected with the FLUTE protocol [START_REF]Digital video broadcasting (DVB); guidelines for the implementation of DVB-IPTV phase 1 specifications; part 5: Content download system (CDS)[END_REF]. Low Density Parity Check (LDPC)-Staircase code is the AL-FEC scheme being chosen along with FLUTE/Asynchronous Layered Coding (ALC) protocol to improve the reliability and efficiency of push video services in the Japanese ISDB-Tmm standard 4 for mobile multimedia [START_REF] Yamada | Overview of isdb-tmm services and technologies[END_REF].

C. Contributions

The question we address in this article is how File delivery protocol (FDP) manages for reliable HbbTV Push-VoD A c c e p t e d m a n u s c r i p t service delivery over broadcast networks. Our contribution is largely methodological contrary to the massive majority of literature studies, which have proposed and/or analyzed different error correction mechanisms within transport protocol under various assumptions or independently of protocol configuration and parameters. The main contributions of this work are summarized as follows:

• First, this paper presents a reference work about the modeling and analysis of inter-layers loss propagation within FDP on a wide variety of burst erasure channels. The developed model enables to determine system performance metrics that helps to understand and effectively dimension different data recovery strategies within FDP. Our analytical model was briefly introduced in a preliminary study in [START_REF] Mattoussi | Analytical modeling of losses in FDP protocol of HbbTV based Push-VoD services over DVB networks[END_REF] and is presented herein in all details with the complete set of mathematical derivations and performance analyses for various system settings. • Second, using the provided analytical analysis on loss propagation within FDP, we define and establish the possible file recovering areas for the coding strategies provided within FDP.

• Third, we propose and investigate a novel solution based on LDPC-Staircase code for FDP protocol to increase the robustness of HbbTV based Push-VoD services delivery over burst-loss channels. This choice of AL-FEC code is based on many interesting key features of LDPC-Staircase as already discussed in [START_REF] Mattoussi | HbbTV based push-vod services over DVB networks: Analysis and AL-FEC code application[END_REF] and shown in details in Section IV. • On this basis, an in-depth analysis of optimal configuration of the coding FDP framework for a reliable VoD delivery over burst-loss channels is provided. Following the approach proposed in [START_REF] Mattoussi | HbbTV based push-vod services over DVB networks: Analysis and AL-FEC code application[END_REF] and [START_REF] Mattoussi | A reliable delivery of HbbTV based Push-VoD services over DVB networks using RS codes[END_REF] a comparison between the provided recovery strategies within FDP is given to determine the best one that guarantees transmission robustness in front of correlated erasure channel impairments. In this paper, an in-depth investigation is carried out while taking into account the correction capacity and the amount of data required to be sent to receive a file correctly.

This paper is organized as follows. An introduction to the FDP protocol and the reliable delivery methods of the Push-VoD services is given in Section II. An investigation and measurement of the loss run distribution within the FDP protocol over a large variety of burst erasure channels is detailed in Section III. A description of different coding strategies and the possible recovering areas within FDP are explained in Section IV. An in-depth analysis of optimal configuration and a performance analysis of the recovery strategies within FDP for a reliable file delivery using FDP protocol is discussed in Section V. Finally, Section VI concludes this paper.

II. HBBTV BASED PUSH-VOD SERVICES

A. Definition

Push-VoD is an established approach to deliver interactive Video-On-Demand (VoD) (i.e., non real-time Audio/Video (A/V) content) services to viewers by providing videos having been previously broadcast and stored on their TV reception equipment. Push-VoD system uses a local storage device (e.g, Set-Top-Box (STB)) to host a wide range of video contents. It works so that the service provider initiates the download of content items from the broadcast to the local storage device automatically and without explicit user request. Once the content is completely downloaded it can be offered for playback to provide an instantaneous and error-free VoD experience. Following this concept, an HbbTV application schedules the download of movies or other audio-visual content prior to its presentation. Moreover, viewers enjoy the benefits of interactivity: they can select and watch whenever they want without waiting time, content that has already been downloaded. The downloaded content is usually deleted after a predefined period to free up space for new content. Push-VoD service is used to provide true VoD and to offload streaming requests to the VoD servers in the network for high demand blockbuster movies and to overcome the problem of broadband connection.

For HbbTV, this service is performed based on the socalled File Delivery Protocol (FDP) and Content Access Download Descriptor (CADD) protocol to broadcast and download the contents respectively [START_REF][END_REF]. Push-VoD provides the highest quality of VoD service even for contents of high data volume (HD, 3D, Ultra HD) and even if a high bandwidth broadband channel is not available [START_REF][END_REF]. The reliable broadcast of HbbTV based Push-VoD services using FDP protocol can be insured using three different methods. The repeat transmission technique of files is the first and simplest way to enable reliable HbbTV based Push-VoD services delivery. The second possible method is the use of a AL-FEC technique which is mathematically a more efficient method of providing repair data and yields better system performance. Finally, HbbTV also enables combining AL-FEC and repeat methods which results in a AL-FEC repeat transmission technique. In each of these three options, file segment interleaving can also be activated to improve robustness against packet losses. Another optional way to achieve the reliability is to use the File segment recovery technique based on the recovery URL via broadband channel. This recovery URL, provided in the Initialization Message, indicates the location where the terminal may retrieve the File segments which have not been received successfully. This technique is based on the terminal-recovery server communication. The terminal shall only use this mechanism in cases where a subset of the File segments of a file has been successfully received, but this subset is not sufficient for the file to be completely reconstructed and there is no broadcast period (i.e., all correction strategies via broadcast channel fail to recover the file) known to the terminal during which missing segments could be received [START_REF][END_REF].

B. FDP description

A VoD service may contain one or more A/V files. According to HbbTV 2.0 specifications, the delivery of each non real time A/V file content is assured using FDP. This protocol enables to generate an FDP stream consisting of FDP messages that end with a CRC to allow the terminal to check the integrity of the received message. Moreover, this stream consists of three categories of FDP messages:

• "Initialization messages": provide information regarding the file (e.g, file identification, file and/or FEC size, File and/or FEC segment size, file recovery URL, etc.) which is necessary for the terminal to initialize its reception.

• "Data messages": make up the A/V file content and may be sent in any order and each one may be sent more than once.

• "Termination messages": are sent after the last "Data message" to indicate to the terminal that this instance of the broadcasting of this file has ended.

All "Data messages" shall be sent between the first "Initialization message" and the first "Termination message". Fig. 1 presents the functional block used to broadcast HbbTV VoD service using FDP. At the transmitter, each A/V file "File Data" undergoes different treatments such as AL-FEC encoding, segmentation, and repetition to generate an FDP stream. This process is more detailed in Fig. 2. If activated, an AL-FEC code is first applied on "File Data" to produce file "FEC Data" containing error correction data that the terminal can use to reconstruct the file in case it has not been properly received. "File Data" and "FEC Data" are both composed of symbols of equal size, symb sz. These files are then divided into segments to generate "File segments" and "FEC segments" respectively. "File segments" (resp. "FEC segments") shall be of equal size, f ile seg sz (resp. F EC seg sz) except for the last "File segment" (resp. "FEC segment") which may be smaller. For a given file, the number of "File segments" and "FEC segments", denoted by N f ile and N f ec respectively, can be determined based on the "File Data" size, f ile sz, and "FEC

N f ile = IN T ( f ile sz -1 f ile seg sz ) + 1, (1)
N f ec = IN T ( F EC sz -1 F EC seg sz ) + 1. (2)
Depending on f ile seg sz and F EC seg sz, each File/FEC segment can contain more than one symbol. The number of symbols per segment, M , may be computed by

M = f ile seg sz (or F EC seg sz) symb sz (3)
In Fig. 2, each File (resp. FEC) segment contains one File (resp. FEC) symbol, i.e. M = 1.

After that each File and FEC segment will be carried in an FDP message of type "Data message". These "Data messages" may be sent in any order and each one may be sent more than once. Then, all FDP messages will be encapsulated within MPEG-4 TS packets according to the Data Piping model of the DVB data broadcasting specification [START_REF][END_REF], as shown in Fig. 2. Depending on FDP message size, F DP msg sz, each FDP message can be carried by one or more MPEG-4 TS packets. The number of MPEG-4 TS packets per FDP message, N can be computed as follows:

N = F DP msg sz M P EG-T S pckt pyld sz (4)
where F DP msg sz equals f ile seg sz (or F EC seg sz) plus the header FDP size and CRC bytes. In Fig. 2, each FDP message is carried by two MPEG-4 TS packets, i.e. N = 2. Moreover, the start of an FDP message may or may not be aligned with the start of the MPEG-4 TS packet payload. In this case, the payload unit start indicator field of the TS packet header shall be used for FDP messages in the same way as specified for PSI sections in ISO/IEC 13818-1 A c c e p t e d m a n u s c r i p t [START_REF]Generic coding of moving pictures and associated audio information-part 1: Systems[END_REF]. As shown in Fig. 1, these MPEG-4 TS packets will be then multiplexed and broadcast with MPEG-4 TS packets carrying linear services. At the terminal, the reverse process will be performed.

III. THEORETICAL MODELING OF LOSSES IN FDP

PROTOCOL Over broadcast networks, MPEG-4 TS packets experience a correlated erasure channel. These packets contain FDP streams that are generated from FDP. Since the recovery strategies work at different levels within FDP (cf. Fig. 2), their behaviors depend on loss patterns appeared at a specific level within FDP rather than MPEG-4 TS packet loss distribution. Therefore, modeling and analysis of interlayers loss spread within FDP on a wide variety of bursty erasure channels is mandatory to determine metrics allowing to measure the loss distortion that helps to understand and efficiently dimension the different recovery strategies within FDP.

In this section, based on a previous introduction of the subject in [START_REF] Mattoussi | Analytical modeling of losses in FDP protocol of HbbTV based Push-VoD services over DVB networks[END_REF], we present a thorough analytical analysis of the loss propagation mechanisms within FDP. To that end, we set up a Markov chain which models the burst losses at various levels of the FDP protocol and whose parameters are derived to be directly expressed from the FDP and lossy channel parameters.

A. Burst-loss modeling

Let us model the loss distribution produced at each FDP system level by defining a Markov chain with appropriate transition probabilities matrix P and steady-state probabilities vector Π. Fig. 3 shows that FDP protocol concept can be represented by three levels where the service content changes shape and size passing from one level to another leading to have different loss dimensions within the protocol. More precisely, each level is characterized by a specific burst loss distribution as detailed and formalized in the following paragraphs.

1) Model at MPEG-4 TS packet level: Since in DVB networks there are as many channels as receivers with features that will also dynamically vary, we propose to use the two-state Markov model known as Gilbert model [START_REF] Gilbert | Capacity of burst-noise channel[END_REF] to characterize the bursty losses over a wide variety of erasure channels. This choice is in line with many works that showed this model to be a good approximation to capture the temporal dependencies of packet losses [START_REF] Sanneck | A framework model for packet loss metrics based on loss runlength[END_REF]. As shown in Fig. 4, this model is characterized by packet transition probabilities (p pckt , q pckt ) between the two states (no-loss (T ) and loss (F )). p pckt is the probability that the next packet is lost, provided the previous one has arrived. q pckt is the opposite. If p pckt + q pckt = 1, the Gilbert model reduces to a Bernoulli model, i.e., erasure channel with Independent and Identically Distributed (IID) losses. Since the Push-VOD service content is broadcast in MPEG-4 TS packet form, the burst loss distribution of these packets is modeled by the two-state Markov chain characterized by packet transition probabilities matrix P pckt and packet stationary probabilities vector Π pckt . The P pckt and the Π pckt are determined as

P pckt = P (T /T ) P (F/T ) P (T /F ) P (F/F ) = 1 -p pckt p pckt q pckt 1 -q pckt (5) and Π pckt = [π pckt (T ) π pckt (F )], (6)
where Π pckt .P pckt =Π pckt . π pckt (T ) and π pckt (F ) represent respectively the packet stationary probabilities for state T and F and are computed by

π pckt (T ) = q pckt p pckt + q pckt π pckt (F ) = 1 -π pckt (T ) = p pckt p pckt + q pckt . (7)
The average MPEG-4 TS packet loss rate (P LR) is given by

P LR = π pckt (F ). (8)
The average burst-loss length (ABL) at MPEG-4 TS packet level can be given by [START_REF] Gilbert | Capacity of burst-noise channel[END_REF]

ABL = ∞ l=1 l.(1 -q pckt ) l-1 .q pckt = 1 q pckt , (9)
where l represents the length of the burst loss. ABL gives the expected mean loss run length.

The average inter-loss distance (AILD) at MPEG-4 TS

MPEG-4 TS packet level FDP message level

Symbol level (N=2) (M=3)

Bursty loss channels (p pckt ,q pckt ) ……. packet level is given by [START_REF] Gilbert | Capacity of burst-noise channel[END_REF]

AILD = ∞ l=1 l.(1 -p pckt ) l-1 .p pckt = 1 p pckt , (10)
where l represents the length of burst no-loss. AILD describes the average distance (spacing) between losses in terms of sequence numbers. It is useful to understand and foretell the spacing between loss events. Consequently, Eq. ( 8) can be determined as follow

P LR = ABL ABL + AILD . ( 11
)
2) Model at FDP message level: An FDP message has a no-loss state iff all the associated N MPEG-4 TS packets have no-loss states. This is defined by a single case denoted by T . An FDP message has a loss state iff at least one of the associated N MPEG-4 TS packets has loss state. There are 2 N -1 possible FDP loss states, depending on the MPEG-4 TS packet losses positions within the FDP message. These cases are denoted by F i , i ∈ {0, . . . , 2 N -2}. Therefore, taking into account Π pckt and P pckt , the loss distribution at FDP message level can be modeled by a Markov chain with two states (T and F = 2 N -2 i=0 F i ) and characterized by its transition probabilities matrix, P r FDP , and its stationary probability vector, Π r FDP . Matrix P r FDP is determined by

P r FDP = P F DP (T /T ) P F DP (F/T ) P F DP (T /F ) P F DP (F/F ) = 1 -p F DP p F DP q F DP 1 -q F DP , (12)
where

p F DP = 1 -(1 -p pckt ) N and q F DP = q pckt .(1 -p pckt ) N -1 .[1 -(1 -p pckt ) N ] p pckt + q pckt .[1 -(1 -p pckt ) N -1 ] . (13)
Vector Π r FDP is given by

Π r FDP = [π F DP (T ) π F DP (F )], (14)
where

π F DP (T ) = q pckt .(1 -p pckt ) N -1 p pckt + q pckt (15) π F DP (F ) = p pckt + q pckt .[1 -(1 -p pckt ) N -1 ] p pckt + q pckt . (16)
Details about probabilities computation can be found in Appendix A.

The average loss rate at FDP message level is equal to π F DP (F ). The average burst loss length at FDP message level (ABL F DP ) is computed by

ABL F DP = 1 q F DP = p pckt + q pckt .[1 -(1 -p pckt ) N -1 ] q pckt .(1 -p pckt ) N -1 .[1 -(1 -p pckt ) N ] . (17)
The average inter-loss distance at FDP message level (AILD F DP ) is computed by

AILD F DP = 1 p F DP = 1 1 -(1 -p pckt ) N . ( 18
)
3) Model at symbol level: As previously mentioned, an FDP message represents an FDP segment composed of M symbols with a header and CRC. Therefore, the loss of an FDP message leads to the loss of all the M associated symbols. The correct receipt of an FDP message leads to the correct receipt of all the M associated symbols. Therefore, the symbol loss distribution can be modeled by a Markov chain with 2M states as shown in Fig. 5 and represented by a transition probabilities matrix P symb as follows

P symb =                           0 1 0 0 . . . 0 0 . . . 0 0 0 1 0 . . . 0 0 . . . 0 0 0 0 . . . . . . 0 0 . . . 0 0 0 0 . . . 1 0 0 . . . 0 1 -p F DP 0 0 . . . 0 p F DP 0 . . . 0 0 0 . . . . . . 0 0 0 0 . . . 0 0 . . . . . . 0 0 1 0 . . . 0 0 . . . . . . 0 0 0 . . . . . . 0 0 . . . . . . 0 0 0 . . . 1 q F DP 0 ... ... 0 1 -q F DP 0 . . . 0                           (19)
The corresponding stationary probabilities vector Π symb is equal to

Π symb = [π symb (T 0 )...π symb (T M -1 )π symb (F 0 )...π symb (F M -1 )], (20)
A c c e p t e d m a n u s c r i p t

with    π F DP (T ) = M -1 i=0 π symb (T i ) π symb (T 0 ) = π symb (T 1 ) = ... = π symb (T ). (21)
Thus, we obtain:

π symb (T ) = 1 M π F DP (T ). (22)
Following the same approach, π symb (F ) is computed as

π symb (F ) = 1 M π F DP (F ). (23)
We may note that the relationship between the FDP message level model and symbol level model is linear according to the M parameter. Therefore, the loss rate at symbol level (SLR) which is equal to that of FDP message level, is computed by using Eq. ( 16) as

SLR = 1 -[(1 -P LR).(1 - 1 AILD ) N -1 ]. (24)
From Eq.( 17), the average burst-loss length at symbol level (ABL symb ) is computed as follows

ABL symb = M. ABL AILD + [1 -(1 -1 AILD ) N -1 ] (1 -1 AILD ) N -1 .[1 -(1 -1 AILD ) N ] (25)
Finally, the average inter-loss distance at symbol level (AILD symb ) is obtained from Eq. ( 18) as

AILD symb = M. 1 1 -(1 -1 AILD ) N . (26)
B. Results and discussions 1) Models validation: In this section, we report some results obtained from numerical method to validate our Markov models proposed above. This validation is based on the comparison between SLR (resp. ABL F DP ) predicted by the proposed theoretical model using Eq. ( 24) (resp. using Eq. ( 17)) and the one estimated through a simulation study by measuring pF DP and qF DP parameters from the realistic loss distribution traces within received data sequences 5 at FDP message level [START_REF] Jiao | On modeling the packet error statistics in bursty channels[END_REF]. These parameters are estimated as follows

pF DP = n-1 i=1 m i m 0 , qF DP = n-1 i=1 m i n-1 i=1 m i .(i) , (27)
where, m 0 is the total number of no-loss FDP messages. m i is the number of loss bursts having length i (i = 1, n -1 and n -1 is the longest burst loss length). Thus, estimations of SLR, ABL F DP and AILD F DP are calculated respectively as follows: 5 For accurate estimation, we consider 10 9 sequences.

SLR = pF DP pF DP + qF DP , ( 28
)
ABL F DP = 1 qF DP , (29)
AILD F DP = 1 pF DP . (30)
Fig. 6 (resp. Fig. 7 and8) gives the SLR comparison (resp. ABL F DP comparison and AILD F DP comparison) over different values of loss patterns at MPEG-4 TS packets (p pckt , q pckt ) for N ∈ {1, 5}. These figures show that the simulation and the theoretical results match perfectly for all values of N and packet loss patterns. The proposed model is then valid at FDP level. Thereby, we can easily conclude it remains valid at symbol level, since we previously demonstrated there is a linear relationship between the two levels.

2) Loss propagation analysis: In this section, based on the proposed models, the loss spread within the FDP protocol is investigated. We determine the effect of the MPEG-4 TS packet loss distribution (measured by P LR, ABL, and AILD) and the FDP system parameters (N and M ) on the loss distribution at symbol-level (measured by SLR, ABL symb and AILD symb ). Theses symbol-level loss metrics enable to predict and understand the behavior of AL-FEC code and to select its good configuration as will be shown in Section V. Fig. 9 depicts the SLR as a function of the P LR, according to Eq. 24, for N ∈ {1, 3, 5} and p pckt ∈ {0.1, 0.5}. As evident from Eq. 24 and the figure, the SLR linearly depends on the P LR according to a positive slope which is directly given by N and p pckt . More precisely, when each FDP message contains one MPEG-TS packet (N = 1), the symbol-level loss rate is equal to MPEG-4 TS packet-level loss rate, i.e. SLR = P LR, regardless the average burst no-loss (AILD) and the average burst-loss (ABL) of MPEG-4 TS packets. On one other hand, for a fixed N , the larger the N and/or p pckt (i.e. the lower the AILD) the higher the SLR. For instance, with AILD = 10 (i.e., p pckt = 0.1) and N = 5, the SLR is equal to 60% for P LR = 40% compared to 74% for P LR = 60%. Eq. (25), we can draw three main conclusions. Firstly, when N = 1, the ABL symb is directly proportional to the ABL independently of the AILD. In such case, the ABL symb will grow according to coefficient M . This is due to the fact that when M = 1, the loss of a segment causes the loss of several consecutive symbols which translates into symbol-level bursts. Second, for a given value of N > 1, the ABL symb varies linearly with the ABL and increases when the AILD decreases (i.e. p pckt increases). Finally, the effect on the ABL symb of increasing system parameter N depends on both the ABL and the AILD. For example, for AILD = 2 (p pckt = 0.5), the increase of N increases the ABL symb for all ABL values. In contrast, for AILD = 10 and AILD = 5 (resp. p pckt = 0.1 and p pckt = 0.2), the increase of N induces different behaviors depending on the ABL value. Fig. [START_REF] Mattoussi | Analytical modeling of losses in FDP protocol of HbbTV based Push-VoD services over DVB networks[END_REF] gives the AILD symb as a function of the AILD, according to Eq. ( 26), for N ∈ {1, 3, 5} with M = 1.

From Eq. (26), it is reminded that the AILD symb only depends on the AILD (i.e., p pckt ) and N parameter. Again, when N = 1, the AILD symb is directly proportional to AILD, with the constant of proportionality equal to M . For N > 1, the increase of the AILD and/or decrease of N yields an increase of the AILD symb which can be approximated as linear for large AILD values. Typically, it is easily concluded that AILD symb → M N AILD when AILD >> 1.

From this performance analysis, we investigate in the sequel of the study how to gauge and configure the coding FDP framework. Indeed, the ABL symb and AILD symb have a direct effect on the file delivery performance, depending on the coding strategies exploited within the FDP protocol. High ABL symb values and small AILD symb values may degrade the effectiveness of coding strategies and may also worsen the final perceptual quality. In the following, we provide a detailed analysis on these aspects. In that perspective, the next section introduces the various coding strategies available at the FDP level.

IV. CODING STRATEGIES WITHIN FDP FOR A FILE DELIVERY

A. Description of coding strategies

For the file download service, it is important to deliver VoD files with a higher level of robustness even under the severe conditions in wireless channels. To address this issue, HbbTV adopts a framework of FDP with one of three coding strategies; employing only repetition code (denoted by Case-1), or only AL-FEC code (denoted by Case-2), or both repetition and AL-FEC mechanisms at the same time (denoted by Case-3). Concerning AL-FEC code, the present document focuses on the so-called LDPC-Staircase code that belongs to the wellknown class of binary structured LDPC codes and whose the construction of their parity check matrices 6 is very simple as described in RFC5170 standard [START_REF] Roca | Low density parity check (LDPC) Staircase and triangle forward error correction (FEC) schemes[END_REF]. As shown in Fig. 12, in addition to length, size, and Pseudo-Random Number Generator (PRNG), this code is characterized by a parameter N1 which defines the degree of source variable nodes. As discussed and briefly analyzed in a previous study [START_REF] Mattoussi | HbbTV based push-vod services over DVB networks: Analysis and AL-FEC code application[END_REF], this kind of AL-FEC code represents a good solution for the FDP protocol to protect the files of the Push-VoD service over HbbTV technology due to many interesting key features such as:

• It is a systematic code and guarantees very high encoding and decoding throughputs [START_REF] Roca | Simple low-density parity check (LDPC) staircase forward error correction (FEC) scheme for FECFRAME[END_REF].

• It shows excellent performance for medium to large object sizes and also perform close to ideal codes in many use-cases when hybrid iterative/maximum likelihood (IT/ML) decoding 7 is performed at the receiver [START_REF] Roca | Low density parity check (LDPC) Staircase and triangle forward error correction (FEC) schemes[END_REF] [21]. • It is a good choice whenever the processing load at a software encoder or decoder must be kept to a minimum even using hybrid iterative/maximum likelihood (IT/ML) decoding [START_REF] Roca | Simple low-density parity check (LDPC) staircase forward error correction (FEC) scheme for FECFRAME[END_REF]. 6 The parity check matrix is subdivided into two parts (H 1 |H 2 ), where H 1 is a sparse matrix with no particular structure, and H 2 is a staircase matrix (i.e., it is the part of redundant symbols) [START_REF] Divsalar | Coding theorems for turbolike codes[END_REF]. 7 Over an erasure channel, ML decoding is equivalent to resolving a linear system using the Gauss elimination (GE) method, which implies a cubic decoding complexity (O(n 3 )). Hybrid decoding, proposed in [START_REF] Paolini | Lowcomplexity LDPC codes with near-optimum performance over the BEC[END_REF], is an appropriate approach that allows a reduced complexity decoder with performance close to the optimal ML decoding. By this approach, we start by IT decoding, and in the case of decoding failure, we proceed with ML decoding (on a smaller-size or more-sparse parity check matrix)

A c c e p t e d m a n u s c r i p t

• It is standardized as RFC5170 with FLUTE)/ALC protocol [START_REF] Paila | FLUTE-file delivery over unidirectional transport[END_REF] to enable a reliable and scalable (no limit on the number of receivers) multicast/broadcast delivery of contents (any kind of files (e.g. multimedia)) over unidirectional transport networks (i.e. without feedbacks) [START_REF] Roca | Low density parity check (LDPC) Staircase and triangle forward error correction (FEC) schemes[END_REF]. It is also standardized as RFC6816 for robust real-time (streaming) delivery services (i.e., broadcasting continuous data stream) in [START_REF] Roca | Simple low-density parity check (LDPC) staircase forward error correction (FEC) scheme for FECFRAME[END_REF]. Moreover, since mid 2012, this code is the AL-FEC scheme included in the ISDB-Tmm Japanese standard for mobile multimedia broadcasting where they are used along with FLUTE/ALC to improve the reliability and efficiency of push video services [START_REF] Yamada | Overview of isdb-tmm services and technologies[END_REF].

This FDP framework is characterized by different parameters which can influence the performance, such as 1) The number of symbols per FDP segment, M: It is a key parameter of FDP. It intervenes on the shape of data sent and thus loss distribution of data which can has a direct impact on the performance of different recovery strategies within FDP. Therefore, we address the problem of the good dimensions of this parameter for the different strategies provided by FDP.

2) The File/FEC segments transmission mode, T x-modecase:

It is a key parameter of FDP. [START_REF][END_REF] precises that File (and FEC) segments may be sent in any order without giving a specific way for different recovery strategies to obtain a reliable FDP. Therefore, a suitable segment transmission mode for a given recovering strategy should be determined. Moreover, the used LDPC-Staircase AL-FEC code creates strong relationships between repair symbols, each repair symbol is the sum of the previous repair symbol with some additional source symbols (see Fig. 12). In that case the subset of received symbols does potentially impact the LDPC-Staircase AL-FEC code performance. Having a good symbol scheduling for LDPC-Staircase AL-FEC code is equivalent to finding a good File/FEC segments transmission mode within FDP.

3) The amount of FEC and/or repetition symbols:

They are key parameters of recovery strategies used within FDP. These two parameters have a significant influence on the FDP performance. In the following section, an in-depth analysis of these parameters is provided to investigate how FDP protocol manages to recover from packet losses using LDPC-Staircase AL-FEC code and/or repetition scheme.

B. Definition of possible recovering areas of recovering strategies

Consider a file composed of k f ile symbols, repetition code and/or AL-FEC code allows to generate n symb symbols. By transmitting these symbols over broadcast network, the number of symbols actually received equals

n rcvd = n symb .(1 -SLR). (31)
To success the file recovery, n rcvd must be at least equal to k f ile (i.e., n rcvd ≥ k f ile ). Based on the channel Gilbert model, we can determine the (p pckt , q pckt ) areas supported by the coding strategies within FDP. Using Eq. ( 24), Eq. ( 8) and Eq. ( 31), the lowest value of q pckt for possible recovering within FDP is given by

q pckt ≥ q pckt,min =p pckt . R (1-p pckt ) N -1 1 - R (1-p pckt ) N -1 , with R =    R rep = 1 Nrep : for Case-1 R F EC = K F EC N F EC : for Case-2 R rep .R F EC : for Case-3 (32)
where respectively K F EC , N F EC , and N rep define the dimension, the length of the AL-FEC code and the number of times of sending k f ile . Fig. 13 provides the areas for possible recovering file for different values of R and N . Fig. 13a shows the areas for N ∈ {1, 2, 3, 5} with R= 1 3 and Fig. 13b shows the areas for R ∈ {1/5, 1/3, 1/2, 2/3} with N = 5. From this figure we can conclude that the increase of R and N reduces the possible file recovering areas of coding strategies provided within FDP. These areas will be used in further analysis.

V. PERFORMANCE ANALYSIS

A. Simulation environment

We evaluate the erasure recovery performance of the HbbTV based Push-VoD services using the FDP protocol. This performance has been assessed through Monte Carlo simulations (10 6 iterations) and are expressed in terms of decoding failure probability and reception overhead ε. The decoding failure probability corresponds to the probability that erased file symbols cannot be all recovered given a set of received symbols. The reception overhead ε measures how many extra symbols over k f ile are needed to recover the file by a receiver. This metric can be defined as follows:

ε = E{r} k f ile -1, ( 33
)
where E{r} is the average amount of necessary symbols that allows to reconstruct the data file and,

k f ile ≤ r ≤      k f ile Rrep : for Case-1 k f ile R F EC : for Case-2 k f ile Rrep.R F EC : for Case-3 (34)
The file recovering will succeed from k f ile (1 + ε) received symbols where, The lower ε, better is the recovery scheme. For perfect code, ε equals to 0. Therefore, k f ile .ε represents the number of symbols over k f ile which are required to success the recovering.

0 ≤ ε ≤ ε max =      1-SLR Rrep -1 : for Case-1 1-SLR R F EC -1 : for Case-2 1-SLR Rrep.R F EC -1 : for Case-3 (35)
To determine the best File (and FEC) segment scheduling for a reliable delivery of Push-VoD services, we introduce different possible transmission modes for each recovering strategy within FDP. Tables I, II, and III show these modes classified into different categories for Case-1, Case-2 and Case-3 respectively. In the sequel, we use f ile sz = 9.2Kbytes and assume that f ile seg sz and F EC seg sz are equal to 920 bytes. In addition, we use M ∈ {1, 5, 10, 20, 40, 184}. For that, Table IV describes number and length in bytes of symbols composed files for each value of M . In addition, based on numerical results showed in [START_REF] Cunche | Optimizing the error recovery capabilities of LDPC-Staircase codes featuring a Gaussian elimination decoding scheme[END_REF], we use N 1 = 5 (cf. Section IV-A) to make a good compromise between the decoding complexity, the improvement of ML decoding, and the degradation of IT decoding. All the results presented in the following sections were obtained by using N = 5. The resulting SLR is given in Fig. 6 and the areas for possible recovering file based on FDP for different values of rate R is shown in Fig. 13b. For instance, for R= 1 3 , the possible recovering area within FDP is started from q pckt,min = 0.27 for p pckt =0.15 and from q pckt,min = 0.11 for p pckt =0.1.

B. Investigation of coding strategies for a file delivery using FDP

The aim of this section is to find out the effect of the different parameters of the FDP framework (cf. Section IV) using the study shown in Section III. Preliminary simulation results given in [START_REF] Mattoussi | HbbTV based push-vod services over DVB networks: Analysis and AL-FEC code application[END_REF] with LDPC staircase codes, and [START_REF] Mattoussi | A reliable delivery of HbbTV based Push-VoD services over DVB networks using RS codes[END_REF] with RS codes, based on a simple Gilbert channel model, have shown the sensitivity of the file delivery mechanisms to such parameters. Therefore, we investigate further the system performance, but exploiting the new expressions derived from the theoretical modeling of losses of FDP protocol presented in Section III. More precisely, we study the effect of changing the number of symbols per segment, M , and the effect of changing the File (and FEC) segments transmission modes, T x-mode-case, for three coding strategies. In addition, we study how many repeated transmissions, N rep , are needed to successfully receive the files for Case-1, and how impact the variation of R rep and R F EC on Case-3 performance.

1) Effect of parameter N rep : This shows the number of repetitions N rep required to rebuild a file using Case-1 based FDP for different packet loss patterns (p pckt , q pckt ). M was fixed to 1 and the File segments are sent randomly.

Fig. 14 depicts the file recovering failure probability as a function of (p pckt ,q pckt ) for N rep ∈ {4, 8, 10}. This figure shows that the needed N rep for low-loss environments is lower than the needed one for high-loss environments. For instance, for 10 -3 as recovering failure probability,

Category (1)

Fully random order Tx-mode-case1=0 all File segments are sent and repeated randomly Category [START_REF][END_REF] File segments are sent sequentially and then repeated in a certain order Tx-mode-case1=1 repeated sequentially Tx-mode-case1=3 repeated randomly Category (3) File segments are sent randomly and then repeated in a certain order Tx-mode-case1=2 repeated sequentially Tx-mode-case1=4 repeated randomly TABLE II: The five File/FEC segment transmission modes (T x-mode-case2) considered for Case-2.

Category (1)

Fully random order Tx-mode-case2=0 all File/FEC segments are sent randomly Category [START_REF][END_REF] File segment are sent first, sequentially, followed by FEC segment in a certain order. Tx-mode-case2=1 FEC segments are sent sequentially Tx-mode-case2=2 FEC segments are sent randomly Category (3) File segments are sent first randomly, followed by FEC segments in a certain order Tx-mode-case2=3 FEC segments are sent sequentially Tx-mode-case2=4 FEC segments are sent randomly TABLE III: The seven File/FEC segment transmission modes (T x-mode-case3) considered for Case-3.

Category (1)

Fully random order Tx-mode-case3=0 all File/FEC segments are sent and repeated randomly Category [START_REF][END_REF] All File/FEC segments are sent sequentially and all then repeated in a certain order. Tx-mode-case3=1 repeated sequentially Tx-mode-case3=3 repeated randomly Category (3) All File/FEC segments are sent randomly and all then repeated in a certain order Tx-mode-case3=2 repeated sequentially Tx-mode-case3=4 repeated randomly File segments are sent first sequentially, followed by FEC segments randomly Category (4) and all then repeated in a certain order Tx-mode-case3=5 repeated sequentially Tx-mode-case3=6 repeated randomly N rep =8 is sufficient for environment with (p pckt = 0.05, q pckt = 0.5) whereas it is not sufficient for that with (p pckt = 0.05, q pckt = 0.1). In addition, from the figure we can notice that performance gets quite poor already with low P LR, ABL and SLR. For example with P LR = 11.11% and ABL = 2.5 (p pckt = 0.05, q pckt = 0.4, SLR = 27.6%, ABL symb = 1.6851) it can take 10 repetitions to receive the file with 10 -4 as recovering failure probability. The increase of N rep improves performance at the cost of increasing total transmission time and E{r}.

2) Effect of parameter M : For this study, all segments are sent randomly (i.e., T x-mode-case1=0 for Case-1, T xmode-case2=0 for Case-2, T x-mode-case3=0 for Case-3).

The use of this transmission mode is chosen so as to mitigate the burst losses which may occur at File (and FEC) segment level and enables to investigate correctly the effect of M . The file recovering failure probability for Case-1 based FDP obtained as a function of (p pckt ,q pckt ) for different M values with N rep =10, is shown in Fig. 15. From this figure we can conclude that a modification of M does not impact the file recovering performance, whatever the packet loss patterns (p pckt , q pckt ). Indeed, additional results not shown in this paper exhibit the same effect on E{r}. As regards Case-2 based FDP, TABLE V and Fig. 16 provide respectively, the decoding failure probability and the reception overhead ε versus packet loss patterns (p pckt , q pckt ) for different M values with R F EC = 1 3 . This table shows that the increase of M increases the decoding failure probability for all (p pckt , q pckt ) values. This is due to the fact that the loss of a segment leads to the loss of M consecutive symbols which causes burst-loss at symbol level and then stucks the LDPC-Staircase decoding. Therefore the increase of M increases the ABL symb (cf. Section III-B2). In addition, an increase of M is equivalent to a decrease symb sz. It is most efficient to keep the symbol size as large as possible (i.e., M is low) so that on the one side, the file won't be protected by a short LDPC-Staircase code which may impact negatively on correction capabilities, and on the other side the total amount of symbols will be low and there will be also fewer lost symbols, which are tried to be recovered in the decoding. For instance, with M = 1 the file consists of 100 symbols of size 920 bytes and protected by a (100, 300) LDPC-Staircase code whereas with M = 40 the file consists of 4000 symbols of length 23 bytes and protected by a (4000, 12000) LDPC-Staircase code. Fig. 16 shows that for low-loss environments the increase of M increases ε for each erasure channel case (p pckt , q pckt ). This is explained by the fact that the decoder needs more data because it is faced with problem of decoding failure as shown in TABLE V. For high-loss environments, M parameter has no impact because the decoder can not succeed the decoding in all cases.

For Case-3 based FDP, Table VI and Fig. 17 illustrate respectively, the result of the decoding failure probability and the reception overhead, ε, as a function of (p pckt , q pckt ) of LDPC-Staircase code (R F EC = 2

3 ) combined with repetition (R rep = 1 2 ) for different M values. Both show that the increase of M does not necessarily lead to increase the decoding failure probability, as seen with Case-2, thanks to the repetition technique. By increasing M

q pckt =0.05 1 1 1 1 1 1 q pckt =0.1 1 1 1 1 1 1 q pckt =0.2 9.96e-1 9.99e-1 1 1 1 1 q pckt =0.35
2.09e-1 9.59e-1 9.99e-1 1 1 1 q pckt =0. [START_REF][END_REF] 8.43e-3 5.66e-1 9.7e-1 9.99e-1 1 1 from 1 to 10, the decoding failure probability has improved and thus the decoder needs fewer symbols. Beyond M =10, the decoding failure probability increases where the decoder needs more symbols to succed decoding.

3) Effect of the Tx-mode-case parameter: In this section, we investigate the impact of File (and FEC) segment transmission modes on the performance of Case-1, Case-2 and Case-3 within FDP. These modes are given in TABLE I, TABLE II and TABLE III for Case-1, Case-2 and Case-3 respectively. M is fixed to 1 to avoid the effect of burst-loss at symbol level induced by M = 1 (see Section. V-B2) and to focus only on the effect of the T x-mode-case parameter. Fig. 18 provides recovering/decoding failure probability of Case-1 (with N rep =10), Case-2 (with R F EC = 1

3 ) and Case-3 (with R F EC = 2

3 ) and R rep = 1 2 ) within FDP as a function of packet loss patterns (p pckt , q pckt ) for different File (and FEC) transmission modes. Fig. 18a shows that T x-mode-case1 has no impact on the file recovery whatever the packet loss pattern (p pckt , q pckt ). From Fig. 18b, we see that transmitting the FEC segments sequentially just after the File segments (sequentially (T xmode-case2 = 1) or randomly (T x-mode-case2 = 3)), leads to very poor results for all packet loss patterns. The reason for this is that with the LDPC-Staircase AL-FEC code, the FEC symbols are produced by following the stairs of parity check matrix of the code (i.e., from the second FEC symbol, each FEC symbol depends on the previous one). In addition, for all packet loss patterns, it appears that T xmode-case2=0, T x-mode-case2=2, and T x-mode-case2=4 are the best and allow to disappear as possible the burstlosses which can be occured at segment level. Fig. 18c shows that, for high loss environment (when p pckt is greater than or equal to 0.10), T x-mode-case3 modes behave exactly the same for all values of q pckt . Whereas, there is a slight difference between T x-mode-case3 modes when p pckt is low (equals to 0.05) and whatever the value of q pckt with the benefit to T x-mode-case3=5. Then T xmode-case3=5 represents the best mode which allows to avoid the problem of burst-loss that can be generated at the File/FEC segment level.

Moreover, Fig. 19 and Fig. 20 illustrate the reception overhead, ε, of Case-2 and Case-3 respectively versus packet loss patterns (p pckt , q pckt ) for the different associated transmission modes. Fig. 19 shows that T x-mode-case2=2 and T x-mode-case2=4 need the lowest reception overhead in all cases. In addition, T x-mode-case2=2 has an additional benefit over T x-mode-case2 = 4 since File segments are sent in sequence, which avoids the extra delay required for the application to submit them all. Fig. 20 shows that T xmode-case3 has an impact on reception overhead only at low-loss environment (cf. Fig. 20a and Fig. 20b). At low-loss environment, it's obvious that T x-mode-case3=0 gives the highest reception overhead since File/FEC segment are sent randomly. For the other T x-mode-case3 modes, Fig. 20a and Fig. 20b show a little difference between the needed reception overhead with the benefits to T x-mode-case3=1 and T x-mode-case3=5 since File segments are sent first sequentially.

4) Effect of parameters R rep and R F EC : The following investigations are with M = 1 and T x-mode-case3 = 0. This choice of parameters allows to mitigate the burst-loss that can occur at symbol level owing to respectively the loss of a segment composed of M symbols and the loss propagation from MPEG-4 TS packet level to FDP message level. Fig. 21 provides the decoding failure probability in Case-3 of LDPC-Staircase code coupled with repetition as a function of packet loss patterns (p pckt , q pckt ) for R F EC ∈ {1/2, 2/3} and R rep ∈ {1/2, 1/4, 1/6}. This figure shows that adding an amount of FEC symbols induces better performance than adding a number of repetitions.

C. Synthesis

When transmitting a file of HbbTV Push-VoD services over a broadcast network, each individual receiver needs to receive all fragments of the file with a low total transmission time and a reasonable error rate so that it can complete the recovery via broadband channel using the File segment recovery technique. Therefore, the required total amount of data and the decoding failure probability represent two key metrics to determine the best coding strategies used within FDP.

q pckt =0.05 1 1 1 1 1 1 q pckt =0.1 1 1 1 1 1 1 q pckt =0.2 1 1 1 1 1 1 q pckt =0.
From the former results, Case-1 based FDP represents the worst case for the same amount of data transmitted in the system. More precisely, according to Fig. 14, Table II and Table III, Case-1 needs a high number of repeat transmission loops to obtain performance equivalent to those of Case-2 or Case-3. In addition, the receivers will likely receive more and more duplicate data as they attempt to obtain their last fragment of the file. In contrast, with Case-2 and Case-3, the file reception progress at the arrival rate of symbols and no time is wasted waiting to receive a specific symbol. Hence, the total amount of data and the time required to deliver files correctly is reduced compared to Case-1. Consequently, Case-1 based FDP causes a transmission with a high amount of data to be sent, and thereby a download time that drastically increases with the symbol loss rate and the file size.

When File/FEC segments are sent randomly, Case-2 based FDP outperforms Case-3 based FDP in terms of decoding failure probability and reception overhead, but only when M is below a certain threshold (in our case below M =10). When M is high, the repetition technique helps Case-3 to reduce the decoding failure probability compared to Case-2. From Fig. 16 and Fig. 17, we observe that Case-2 needs more symbols and so more download time than Case-3 to succeed in the decoding step when M is greater than 10. By using the best File/FEC segments transmission mode in each case, we can conclude that Case-2 achieves better decoding failure probability and requires a lower reception overhead than that of Case-3 whatever the loss-environment (see. Fig. 18b vs Fig. 18c and Fig. 19 vs Fig. 20). Regarding the recovery complexity, Case-3 has lower com-plexity than Case-2 since the former needs fewer operations and the repetition does not yield any additionnal complexity. To exceed Case-2, Case-3 needs more repeat transmission loops leading to high data rate and file recovery time.

VI. CONCLUSION

In this paper, we focused on the HbbTV based Push-VoD services transmitted over DVB networks using the FDP protocol. This protocol is characterized by three levels of data representation and includes different coding strategies to ensure a reliable delivery. Due to these levels, the data shape and size change within this protocol give rise to three loss distributions that may affect the coding strategies behaviors. This article presents a reference work on the full feature investigation of FDP and how it handles a reliable file delivery on a wide variety of burst-erasure channels. Contrary to the massive majority of literature studies on the analysis of error correction mechanisms within transport protocols, our contribution is largely methodological and includes four main contributions.

• First of all, we presented a thorough analytical analysis, based on a Markov chain, of the inter-layers loss spread within FDP on a wide variety of burst-erasure channels. This analysis enabled us to determine metrics allowing to measure the loss-run that helps to understand and tune effectively within FDP the different recovery strategies. • Then, this study allowed to determine the possible file recovering areas for a coding strategy within FDP. We proposed and analyzed a first AL-FEC solution for a reliable Push-VoD service delivery via FDP over burstloss channels. This solution is based on LDPC-Staircase codes due to its many interesting key features. correction capability and amount of data required to be sent to correctly receive a file. This study showed that FDP's parameters shall carefully be chosen to ensure a reliable broadcast of Push-VoD service. • Finally, the suitable coding strategy within FDP that guarantees transmission robustness in front of correlated erasure channel impairments was presented. This study reveals that LDPC-Staircase AL-FEC code achieves the best trade-off between correction complexity, file recovering and download time compared to other recovery strategies provided by FDP.

Eventually, this paper provides an efficient model to assess the performance of the HbbTV system for non-linear service delivery using FDP. A detailed analysis was proposed to highlight the impact of the main parameters of the system with the example of an LDPC staircase AL-FEC. The developped analytical tools can be further exploited for the optimization of any other AL-FEC strategy, combined or not with repetion and segmentation processes.

APPENDIX A BURST-LOSS MODELING AT FDP MESSAGE LEVEL

Let us consider two consecutive FDP messages with states S 1 and S 2 . Since each FDP message consists of N MPEG-4 TS packets, so S 1 ={s 1,k , k = 0, N -1 1 8 } and S 2 ={s 2,k , k = 0, N -1}. s 1,k and s 2,k represent the state of the kth MPEG-4 TS packet within an FDP message with state S 1 and S 2 respectively. Therefore, the transition probability from S 1 to S 2 can be calculated as:

P (S2/S1) = prob(s2,0/s1,N-1).

N -1 k=1 prob(s 2,k /s 2,k-1 ), (36) 8 0, N -1 represents the set of integers from 0 to N-1.

and the stationary probability of an FDP message with state S 1 is computed as:

πF DP (S1) = P (S1) = prob(s1,0).

N -1 k=1 prob(s 1,k /s 1,k-1 ),

where prob(s 1,0 ) and prob(s i,k /s j,k-1 ) are determined from Π pckt and P pckt respectively. The π F DP (S 2 ) is calculated in the same manner.

An FDP message has a no-loss state iff all the associated N MPEG-4 TS packets have no-loss states. This is defined by a single case denoted by T . An FDP message has a loss state iff at least one of the associated N MPEG-4 TS packets has loss state. There are 2 N -1 possible FDP loss states, depending of the MPEG-4 TS packet losses positions within the FDP message. These cases are denoted by F i , i ∈ {0, . . . , 2 N -2}. Therefore, we can model the FDP messages distribution by a Markov chain with 2 N states characterized by the stationary probabilities vector Π FDP = [π F DP (T ), π F DP (F 0 ), . . . , π F DP (F 2 N -2 )], (38) where π F DP (T ) and π F DP (F i ) are calculated using Eq. (37), and a transition probabilities matrix, P FDP composed of (2 N ) 2 transition probabilities computed using Eq. (36). This model can be reduced to a Markov chain with two states (T and F =

where Π r FDP .P r FDP =Π r FDP and π F DP (T )+π F DP (F )=1. The stationary probability of an FDP message with noloss state (T ) is computed using Eq. ( 6) as follows:

π F DP (T ) = π pckt (T )(P pckt (T /T )) N -1 = q pckt (1 -p pckt ) N -1 p pckt + q pckt (41)

Therefore, the stationary probability of an FDP message with loss state (F ) is given by:

π F DP (F ) = 2 N -2 i=0 π F DP (F i ) = 1 -π F DP (T ) = p pckt + q pckt [1 -(1 -p pckt ) N -1 ] p pckt + q pckt (42)
The transition probability P F DP (T /T ) is calculated using Eq. (36) as follows:

P F

Fig. 1 :

 1 Fig. 1: Functional block for broadcasting HbbTV VoD service.

Fig. 3 :

 3 Fig.3: The overall MPEG-4 TS packet to symbol loss mapping in FDP system. Red color represents the losses at each level.

Fig. 4 :

 4 Fig. 4: Two-state Markov model.

Fig. 5 :

 5 Fig. 5: The Markov model with 2M states for symbol loss distribution.

Fig. 6 :

 6 Fig. 6: Comparison of the theoretical and simulated values of the SLR for N ∈ {1, 5}.

Fig. 10

 10 Fig.6(resp. Fig.7 and 8) gives the SLR comparison (resp. ABL F DP comparison and AILD F DP comparison) over different values of loss patterns at MPEG-4 TS packets (p pckt , q pckt ) for N ∈ {1, 5}. These figures show that the simulation and the theoretical results match perfectly for all values of N and packet loss patterns. The proposed model is then valid at FDP level. Thereby, we can easily conclude it remains valid at symbol level, since we previously demonstrated there is a linear relationship between the two levels.2) Loss propagation analysis: In this section, based on the proposed models, the loss spread within the FDP protocol is investigated. We determine the effect of the MPEG-4 TS packet loss distribution (measured by P LR, ABL, and AILD) and the FDP system parameters (N and M ) on the loss distribution at symbol-level (measured by SLR, ABL symb and AILD symb ). Theses symbol-level loss metrics enable to predict and understand the behavior of AL-FEC code and to select its good configuration as will be shown in Section V. Fig.9depicts the SLR as a function of the P LR, according to Eq. 24, for N ∈ {1, 3, 5} and p pckt ∈ {0.1, 0.5}. As evident from Eq. 24 and the figure, the SLR linearly depends on the P LR according to a positive slope which is directly given by N and p pckt . More precisely, when each FDP message contains one MPEG-TS packet (N = 1), the symbol-level loss rate is equal to MPEG-4 TS packet-level loss rate, i.e. SLR = P LR, regardless the average burst no-loss (AILD) and the average burst-loss (ABL) of MPEG-4 TS packets. On one other hand, for a fixed N , the larger the N and/or p pckt (i.e. the lower the AILD) the higher the SLR. For instance, with AILD = 10 (i.e., p pckt = 0.1) and N = 5, the SLR is equal to 60% for P LR = 40% compared to 74% for P LR = 60%. Fig. 10 provides the ABL symb as a function of the ABL, according to Eq. (25), for N ∈ {1, 3, 5} and p pckt ∈ {0.1, 0.2, 0.5} with M = 1. From this figure and

Fig. 7 :

 7 Fig. 7: Comparison of the theoretical and simulated values of the ABL F DP .

Fig. 8 : 5 Fig. 9 :A c c e p t e d m a n u s c r i p tFig. 10 : 1 AILDFig. 11 :

 85910111 Fig. 8: Comparison of the theoretical and simulated values of the ABL F DP .

Fig. 12 :

 12 Fig. 12: Parity check matrix of LDPC-Staircase codes as defined in RFC5170 standard.

Fig. 13 :

 13 Fig. 13: Possible file recovering areas within FDP. (a) for various values of N and R = 1 3 . (b) for various values of R and N = 5.

1 Fig. 14 :

 114 Fig. 14: Effect of N rep parameter variation in Case-1 based FDP versus loss patterns (p pckt , q pckt ) with M = 1.

  A c c e p t e d m a n u s c r i p t

Fig. 15 :

 15 Fig. 15: Effect of parameter M on the recovering failure probability in Case-1 based FDP versus loss patterns (p pckt , q pckt ) with N rep = 10.

p pckt =0. 15 Fig. 16 :

 1516 Fig. 16: Effect of parameter M on the reception overhead in Case-2 based FDP versus loss patterns (p pckt , q pckt ) with R F EC = 1 3 . (a) for p pckt = 0.05, (b) for p pckt =0.1, and (c) for p pckt = 0.15.

3 Fig. 18 :

 318 Fig.18: Effect of the T x-mode-case parameter variation on the recovering/decoding failure probability versus packet loss patterns (p pckt , q pckt ) .

1 R 1 R 15 Fig. 21 :

 111521 Fig. 21: Effect of R rep and R F EC parameters on decoding failure probability under different loss patterns (p pckt , q pckt ) in Case-3.

2 N - 2 i=0F

 2 i ) and characterized by the transition probabilities matrixP r FDP = P F DP (T /T ) P F DP (F/T ) P F DP (T /F ) P F DP (F/F ) = 1 -p F DP p F DP q F DP 1 -q F DP ,(39)and the stationary probability vector Π r FDP = [π F DP (T ), π F DP (F )],

  DP (T /T ) = (P pckt (T /T )) N = (1 -p pckt ) N = 1 -p F DP .(43)A c c e p t e d m a n u s c r i p t

TABLE I :

 I The five File segment transmission modes (T x-mode-case1) considered for Case-1.

TABLE IV :

 IV The symb sz and the number of symbols composed files versus M parameter for f ile sz = 9.2Kbytes and f ile seg sz=F EC seg sz = 920 bytes.

	M	1	5	10	20	40	184
	symb sz(bytes)	920	184	92	46	23	5
	Number of sym-	100	500	1000	2000	4000	184000
	bols

TABLE V :

 V Effect of parameter M on the decoding failure probability in Case-2 based FDP versus loss patterns (p pckt , q pckt ) with R F EC = 1 3 .

	(p pckt ,q pckt )	M	1	5	10	20	40	184
		q pckt =0.05	1.74e-3	4.42e-1	9.74e-1	9.99e-1	1	1
	p pckt =0.05	q pckt =0.1 q pckt =0.2	1.3e-5 0	3.58e-4 5e-6	6.05e-4 1.2e-5	2.08e-2 2.95e-4	4.52e-1 6.23e-4	1 3.12e-1
		q pckt =0.35	0	2.66e-6	5e-6	1.2e-5	7e-5	4.33e-3
		q pckt =0.5	0	0	0	9.99e-6	1.5e-5	1.8e-3
		q pckt =0.05	1	1	1	1	1	1
	p pckt =0.1	q pckt =0.1 q pckt =0.2	8.7e-1 4.27e-4	9.99e-1 8.41e-2	9.99e-1 6.39e-1	1 9.91e-1	1 9.99e-1	1 1
		q pckt =0.35	4.7e-5	9.97e-4	7.74e-3	2.53e-1	8.95e-1	1
		q pckt =0.5	9e-6	2.96e-4	6e-4	2.23e-2	4.17e-1	9.99e-1
	p pckt =0.15

TABLE VI :

 VI Effect of parameter M on the decoding failure probability in Case-3 based FDP versus loss patterns (p pckt ,q pckt ) parameters with R F EC = 2 3 , R rep = 1 2 .

	(p pckt ,q pckt )	M	1	5	10	20	40	184
		q pckt =0.05	8.56e-1	8.41e-1	8.39e-1	8.44e-1	8.69e-1	9.69e-1
	p pckt =0.05	q pckt =0.1 q pckt =0.2	1.21e-3 3.5e-5	2.74e-4 1e-5	8.19e-4 9.99e-6	2.65e-3 8.6e-5	6.93e-3 1.62e-4	1e-1 1.47e-3
		q pckt =0.35	3.2e-6	1.96e-6	0	1.76e-5	3.99e-5	9.2e-5
		q pckt =0.5	1e-6	0	0	1.59e-5	3.99e-5	9.2e-5
		q pckt =0.05	1	1	1	1	1	1
	p pckt =0.1	q pckt =0.1 q pckt =0.2	9.99e-1 4.24e-1	9.99e-1 3.66e-1	1 3.65e-1	9.99e-1 3.85e-1	9.99e-1 4.63e-1	1 8.26e-1
		q pckt =0.35	7.76e-3	1.81e-3	3.9e-3	9.42e-3	2.88e-2	2.73e-1
		q pckt =0.5	1.19e-3	2.76e-4	7.77e-4	2.60e-3	6.9e-3	1
	p pckt =0.15

  Effect of parameter M on the reception overhead in Case-3 based FDP versus loss patterns (p pckt , q pckt ) with R F EC = 2 3 and R rep = 1 2 .

	1.2	Case-3 (R FEC =2/3, R rep	=1/2), Tx-mode-case3=0
	0.25 0 A c c e p t e d 0.3 0.35 0.4 0.45 m 0.5 q pckt 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.2 (a) p pckt =0.05 q pckt 0.15 0.2 0.25 0.3 0.35 0.4 Reception overhead, ǫ 0.1 0.2 0.3 0.4 0.5 0.6 Case-3 (R FEC =2/3, R rep =1/2), Tx-mode-case3=0 M=1 M=5 M=10 M=20 M=40 M=184 ǫ max (b) p pckt =0.1 0.05 Reception overhead, ǫ 0.1 0.15 0.2 Case-3 (R FEC =2/3, R rep =1/2), Tx-mode-case3=0 M=1 M=5 M=10 M=20 M=40 M=184 ǫ q pckt 0.05 0.1 0.15 0.2 0.25 0.3 a n u s c r i p t 0.35 0.4 0.45 Reception overhead, ǫ 0.4 0.6 0.8 1 M=1 M=5 M=10 M=20 M=40 M=184 ǫ max Recovering failure probability
		q pckt

• Thereafter, an in-depth analysis of the configuration of coding FDP framework for a reliable Push-VoD service delivery over burst-loss channels was provided. We investigated the effect of different parameters in each coding strategy within FDP taking into account max (c) p pckt =0.15 Fig.

17:

DSM-CC is used to deliver Internet data via the broadcast channel. The DSM-CC allows to transmit small applications (like teletext replacement) to viewers who do not connect their devices to the Internet, by minimizing web server load by transmitting a small autostart launcher application and link to web resources in a second usage step. However the conventional way of accessing HbbTV applications is by a HTTP request from a broadbandconnected service.

[START_REF][END_REF] set of files comprising an application, including HTML, Javascript, CSS and non-streamed multimedia files

FLUTE, defined in RFC 3926, is a protocol for the unidirectional delivery of files over the Internet, which is particularly suited to multicast networks. Its main characteristics is that this protocol offers reliability in the transmission. DVB-H uses FLUTE to send the Electronic Service Guide (ESG).

This is a broadcast technology (based on ISDB-T), used for digital terrestrial TV services and suited to mobile environments.

This work has received a French state support granted to the AdicTV project through the 20th FUI (transverse inter-ministry funding) program. The authors would also like to thank the "Image&Réseaux" and "Cap Digital" french business clusters for their support of this work.

Consequently, the transition probability P F DP (F/T ) is given by:

The transition probability P F DP (T /F ) is computed by:

Whereas, by ordering F i so that F i ends with a packet with F state when i = 0, 2 N -1 -1 and with a packet with T state when i = 2 N -1 , 2 N -2 we can obtain that:

Using Eq. (41), Eq. ( 46) and Eq. (47), Eq. ( 45) becomes:

Consequently, the transition probability P F DP (F/T ) is given by: