James A Isaac

Aurore Thibon-Pourret

Amélie Durand

Christian Philouze

Nicolas Le Poul
email: nicolas.lepoul@univ-brest.fr

Catherine Belle
email: catherine.belle@univ-grenoble-alpes.fr

High-valent Cu II Cu III Species in Action: Demonstration of Aliphatic C-H Bond Activation at Room Temperature

The electrochemically generated Cu II Cu III mixed-valent species promotes activation of strong aliphatic CH bond (i.e. toluene) at room temperature. The mechanistic pathway turns from stoichiometric to catalytic upon addition of base, hence demonstrating that such high-valent dicopper species can be key reactive intermediates in copper-based oxidative processes.

we have taken advantage of an electrochemical approach as a more environmentally friendly solution 9 avoiding stoichiometric chemical oxidants.

Mild, efficient and direct routes for C-H oxidation/oxygenation to form industrially valuable products is of considerable interest in addressing mild and sustainable synthetic procedures and current energy concerns. 1 In this context, copper-based catalysts appear as good alternatives to precious metal because of its natural abundance, low toxicity and low-cost nature. Hence, various copper-based catalysts have been developed using O 2 as terminal oxidant. 2 Biomimetic approaches have proven to be very helpful by elucidating the nature of oxido, hydroxido, peroxido or superoxido copper intermediates able to mediate C-H bond activation. Each of them displays distinct abilities for oxidation-oxygenation including cross coupling reactions as described in several reviews. 3 Among them Cu II Cu III mixed-valent species have been previously suggested as possible intermediates for C-H bond activation. 3f, 4 Challenges remain to explore the capability of such species in oxidation as examples are scarce 5 and only one 5a demonstrated C-H bond activation on a fairly weak bond (i.e. dihydroanthracene).

Dipyridylethane naphthyridine (L) and its analogs act as compartmental ligands and have allowed the isolation of dinuclear complexes with metallic centers in close proximity. 6 Recently, from L as bridging ligand, we have prepared the dinuclear copper(II) complex 1 ([Cu ). 7 Because of the presence of a triflate anion at one copper site, the two Cu atoms are not in identical 8 The data suggest that the hydroxido bridges remain coordinated and protonated after the mono-oxidation into 1 + .

We have initiated our studies by probing the behavior of the starting complex 1 in the presence of an excess of ClO 4 -since our voltammetric studies have been carried out in NBu 4 ClO 4 /CH 3 CN. After slow evaporation, crystals of

[Cu II 2 (L)(µ-OH) 2 ](ClO 4 ) 2 •6H 2 O (2•6H 2 O
) suitable for X-ray analysis (details in ESI) were obtained, hence evidencing the removal of the triflate anion in the copper coordination sphere. The symmetrical entity 2 obtained (Fig. 1) displayed similar metrical parameters to those of 1 (Table S1) with a slightly longer Cu…Cu distance (2.793 Å vs. 2.751 Å in 1) and both Cu atoms in square pyramidal geometry. This result suggested that 1 and 2 are equivalent upon dissolution into acetonitrile in presence of ClO 4 -. To explore the capability of 1

+ to perform C-H activation, So far, copper-based electrochemical studies have been restrained to water oxidation or oxygen/CO 2 reduction 11 and this strategy has not be explored for the catalytic oxidation of strong C-H bonds by copper species.

We then focused our studies on the oxidation of toluene (Bond dissociation energy (BDE) = 89.8 kcal•mol -1 ) 12 by the electrochemically generated complex 1 + . The direct oxidation of the aliphatic C-H bond in toluene is faced by several drawbacks such as high temperatures and pressures and by-products. 13 Rare examples have been reported

from bio-inspired models involving Cu 2 /O 2 intermediates 14 possibly in confined environment. 15 Furthermore, to date, catalytic turnover is still regarded as a challenge. Cyclic voltammetry (CV) of the dicopper(II) complex 1 in NBu 4 ClO 4 /CH 3 CN is shown in Fig. 2 (blue curve). The complex exhibits a quasi-reversible system at E 1/2 (1) = 1.12 V vs. Fc + /Fc which can be ascribed to the 11 + reaction from our previous studies. 7 At very low scan rate (0.02 V.s -1 , Fig. S2), the cathodic to anodic peak current ratio (i pc /i pa ) decreases due to the probable reaction of the oxidized species with the solvent, as reported. 7 As shown in Fig. 2, S2 and S3, a significant loss of reversibility was observed upon addition of toluene-H8 (110 to 500 mol. equiv.), within the studied scan-rate range (0.02 V.s

-1 < v < 0.2 V.s -1
). This result suggested us that the Cu II Cu III species 1 + reacts with that substrate. Experiments performed with toluene-D8 also led to a decrease of the cathodic peak current but in a less pronounced manner (Fig. Electrolysis of 1 in NBu 4 ClO 4 /CH 3 CN with toluene in excess (490 equiv.) followed by purification and analysis by GC-MS (see ESI, Fig. S5) allowed the oxidation products of toluene to be determined. Among them, benzaldehyde, benzyl alcohol, benzylacetamide, 2-(methylphenyl)-toluene and 4-(methylphenyl)-toluene were detected, consistent with a radical processes involving Ph-CH 2  formation, recombination or attack at nitrogen on the solvent. 16 In order to determine the possible O atom source, an exhaustive electrolysis of 1 was performed in a solution of NBu 4 ClO 4 /CH 3 CN containing H 2 [START_REF] Dhar | [END_REF] O under argon (details in ESI, Fig. S6 and Table S2). Analysis by GC-MS evidenced that [START_REF] Dhar | [END_REF] O from added water was incorporated into benzyl alcohol, benzaldehyde and benzylacetamide along with non-labelled O atom, hence suggesting that oxygen atom transfer may also involve others sources (hydroxido bridge or residual water).

Having demonstrated that the Cu II Cu III species is reactive towards the strong aliphatic CH bond of toluene, we then focused our efforts on making the system catalytic. Presumably, the reaction of 1 + with toluene leads to the formation of an inactive (µ-OH)(OH 2 )Cu II Cu II species through a proton-coupled electron transfer (PCET).

Investigations were therefore carried out using 2,6-lutidine(Lut) with the aim of regenerating the bis(µ-OH)Cu II Cu II core from the (µ-OH)(OH 2 )Cu II Cu II adduct. First studies were performed in absence of toluene in order to investigate the oxidative properties of the species resulting from the oxidation and deprotonation of 1. CVs of 1 in NBu 4 ClO 4 /CH 3 CN upon addition of 2,6-lutidine are displayed in Fig. 3. A dramatic rise in the current was observed with increasing the concentration in Lut, symptomatic of an electrocatalytic wave. A pre-peak was detected at ca. E pa (2) = 1.05 V vs. Fc + /Fc for sub-stoechiometric amounts of Lut. The potential of the pre-peak increased upon further addition of Lut, whereas the potential of the second peak at E pa (1) = 1.15 V vs. Fc + /Fc assigned to the oxidation of 1 to 1 + remained constant. These CVs are typical of a "total catalysis" redox behavior involving a (co)substrate-diffusion-controlled catalytic reaction (pre-peak), as well as a catalyst-diffusion-controlled process (second peak). 9b, 10c, 17 To rationalize this behavior, bulk electrolysis of 1 was carried out in excess of 2,6-lutidine (8 equiv. vs. 1).

1 H-NMR analysis of the resulting products indicated that the methyl groups of the 2,6-lutidine were not oxidized (Fig. S7). Addition of water induced a slight increase of the catalytic current up to around 10 equiv. until to reach a plateau, consistent with the recovering of hydroxido bridges (Fig. S8). Hence, these results strongly suggest that acetonitrile acts as substrate for the electrocatalytic reaction in presence of base.

In order to further analyze this redox behavior, plots of i pa (2) vs.

[Lut] (from CVs displayed in Fig. 3) and i pa (2) vs. v 1/2 (from CVs displayed in Fig. 4), allowed the bounds of the total catalysis regime to be determined (i pa ( 2) is defined as the anodic peak current at E pa ( 2)). 9b A straight-line variation was obtained from plots of i pa ( 2) vs. v 1/2 for 5 < v < 100 mV · s -1 (Fig. S10B). Moreover, the i pa ( 2) vs.

[Lut] plot deviates from a straight-line at a 2,6-lutidine concentration greater than 1.5 equiv. (Fig. S10A). As the criteria for a total catalysis were fulfilled in the CVs displayed in Fig. 3, the number of electrons involved was extracted from the plot of pre-peak current against the square root of the scan rate [START_REF] Costentin | Proc. Natl. Acad. Sci[END_REF] (see ESI). The calculations indicated a mono-electronic process. Given this, a peak shift analysis of the data displayed in Fig. 4 was performed for the determination of the kinetics of the catalytic reaction (see ESI, Fig. S11). Noteworthy, the calculated rate constant value (k obs = 6 × 10 4 M -1 · s -1 ) was significantly higher than that of the stoichiometric reaction of 1

+ with toluene H8 (1.1 M -1 · s -1
, see above). To further investigate the effect of the base, voltammetric simulations were carried out according to an EC 1 C 2 C 3 C 4 mechanism (Scheme 1, details in ESI). After electrochemical oxidation (step E), two chemical reactions are competing (C 1 and C 2 ): that of the electrogenerated Cu II Cu III 1 + species with the substrate SH (here SH = CH 3 CN as no toluene is present in this experiment) (step C 1 ) which probably yields a radical S

• species together with a dicopper(II) hydroxido aqua complex, and that of 1 + with 2,6-lutidine to form species A (step C 2 ). Species A then reacts with SH (step C 3 ) to regenerate the bis(µ-OH)Cu II 2 species, according to a catalytic pathway. Finally the step C 4 was added to account for the reaction of S

• with the bis(µ-OH)Cu II Cu III species, making the oxidation peak at E pa (1) irreversible, as experimentally observed. A good match between the simulated and the experimental curves (Fig. S12) was obtained by considering the steps C 2 (deprotonation of 1 + ) and C 3 (oxidation of the substrate) as very fast, in agreement with a "total catalysis" case. Best fits were found for rate ). These voltammetric studies clearly demonstrate that the addition of base (i) triggers the mechanistic pathway from a stoichiometric reaction to a catalytic one, and (ii) enhances by a four-order magnitude the rate constant of the oxidation of the CH bond. Different active species, namely Finally, the same catalytic experiments were performed with addition of toluene which did not induce any significant modification of the voltammetric response. However, bulk electrolysis of the toluene-based solution led to the formation of benzaldehyde, benzyl alcohol and benzylacetamide, although the yield in oxidized products from toluene is low as shown by GC analysis (see details in ESI and Fig. S13). Such a result is consistent with the fact that both toluene and acetonitrile display close BDE values (89.8 and 93 kcal•mol -1 respectively) and can both be oxidized by species A. In summary, we have demonstrated that a Cu II Cu III species reacts with toluene in a single turnover reaction, functionalizing the aliphatic CH bonds in the RDS. The addition of a base renders the system catalytic even without toluene suggesting that CH 3 CN acts as a substrate. In this case, the observed rate constant determined to be 6 × 10 and Fig S14). Future work will be focused on characterizing the transient active species responsible for CH activation and optimizing this system, mainly by tuning the pKa and redox potential of the complexes. [START_REF] Dhar | [END_REF] This breakthrough should be further developed for expanding the scope of selective and sustainable oxidation reactions.

II 2 (

 2 L)(µ-OH) 2 (OTf)](OTf) where OTf -= CF 3 SO 3 -

Fig. 1

 1 Fig. 1 ORTEP of the cationic part of [Cu II 2(L)(µ-OH)2](ClO4)2•6H2O (2•6H2O)(50% probability ellipsoids). H atoms (except from the OH) have been omitted. See ESI for details

Fig. 2

 2 Fig. 2 CVs of 1 (1.2 mM) upon the addition of toluene-H8 (black) or toluene-D8 (red); 0.1 M NBu4ClO4/CH3CN at 20°C under Ar.

  2), indicating a kinetic isotope effect (KIE). Voltammetric simulation of the CVs allowed the determination of the forward rate constant, k f , for the chemical oxidation of toluene by 1 + (details in ESI, Scheme S1 and Figs S2-S3). The experimental behavior was reproduced for different values of substrate concentration and different scan rates. We found that k f = 1-and D8-toluene, respectively, yielding a KIE value k f (H)/k f (D) = 2.2. It indicates that the rate determining step (RDS) involves cleavage of the CH bond of the substrate upon electrochemical oxidation of 1. However, the reaction remains stoichiometric and not catalytic, as shown by the comparable anodic peak current i pa (1) values obtained in absence and presence of toluene (Fig. S4).

Fig. 3

 3 Fig. 3 CVs of complex 1 (0.8 mM) upon addition of 2,6-lutidine (Lut). 0.1 M NBu4ClO4/CH3CN; [Lut] = 0.3, 0.6, 1.2 and 2.4 mM at 20°C under Ar.

Fig. 4

 4 Fig.4 CVs of 1 (0.8 mM) with [Lut] = 0.6 mM at different scan rates; 0.1 M NBu4ClO4/CH3CN at 20°C under Ar.

Scheme 1 . 3 )

 13 Scheme 1. EC1C2C3C4 proposed mechanism used for voltammetric simulations (details in ESI). constant values of k f (C 2 ) = 7±1  10 5 and k f (C 3 ) = 10±1  10 5 M -1 · s -1 . These values are comparable with that

Scheme 2 .

 2 Scheme 2. Electrochemical SH activation by 1 without or with 2,6-lutidine (Lut).

  1 + and A, are involved for the stoichiometric and catalytic oxidation of the substrates, respectively (Scheme 2). Although the species A has not been isolated, we propose that deprotonation of 1 + occurs on one of the bridging OH groups, leading to an oxido hydroxido Cu II Cu III species (A) (Scheme 2). Deprotonation of the µ-OH group is indeed more favored for 1 + than 1, because of the probable decrease of the pKa of the oxo/hydroxido group at the Cu(III)-Cu(II) redox state (vs. Cu(II)-Cu(II)).

  Cu III cores can be active species for oxidation of methane to methanol. 4a To the best of our knowledge, this work is the first electrochemically copper-catalyzed CH oxygenation and in addition operating in mild conditions. This proof of concept study demonstrates the oxidative reactivity of Cu II Cu III species towards exogenous substrates and has shed light on such high-valent species as new potent catalytic motifs in oxidative attack of strong sp 3 CH bonds. The electrochemical C-H activation described in this work appears to be selective as no aromatic C-H activation is observed. Furthermore with ethylbenzene as alternative substrate only the benzylic position is activated (see details in ESI

	4 M oxido hydroxido Cu -1 · s -1 was refined through simulations to give a value of 7±1  10 II Cu	5 M	-1 · s	-1 , and alludes to a possible

III

(A) as the active species. It is in agreement with the previous proposal that (µ-O)(µ-OH)Cu II

The authors gratefully acknowledge C. Costentin for fruitful discussion about this work. The French research agency is acknowledged for support (ANR-13-BSO7-0018) and ICMG FR 2607 (PCN-ICMG).This work has been partially supported by Labex ARCANE (ANR-11-LABX-0003-01) and CBH-EUR-GS (ANR-17-EURE-0003).

Conflicts of interest

There are no conflicts to declare.

Notes and references


F Gunsing

F Belloni

E Berthoumieux

M Diakaki

E Dupont

E Ferrer-Ribas

Th Papaevangelou

MicroMegas-based detectors for time-of-flight measurements of neutron-induced reactions

MicroMegas detectors are versatile gaseous detectors which are used for ionizing paricle detection. A MicroMegas detector consists of two adjacent gas-filled volumes. One volume acts as a drift region with an electric field operating in the ionization chamber regime, the second volume is the amplification region acting as a parallel-plate avalanche counter. The use of the microbulk technique allows the production of thin, radiation resistant, and low-mass detector with a highly variable gain. Such MicroMegas detectors have been developed and used in combination with neutron time-of-flight measurements for in-beam neutron-flux monitoring, fission and light-charged particle reaction cross section measurements, and for neutron-beam imaging. An overview of MicroMegas detectors for neutron detection and neutron reaction cross section measurements and related results and developments will be presented.

Introduction

Since the development of the first prototype, MicroMegas detectors [1] are used in many experiments in nuclear and particle physics. The MicroMegas detector was originally developed to cope with issues under high count rates with existing gaseous detector families used in highenergy physics. At present MicroMegas detectors are widely used in a variety of shapes [START_REF]Scintillations 97-98[END_REF]. These detectors have usually good position and timing properties thanks to the oftenly applied granular readout, have an excellent radiation hardness. and can cover large or even curved surfaces. Some examples of their use in high-energy experiments are CLAS12, ALTAS-NSW, and T2K. Other experiments concern X-ray detection from solar axions with the CAST project [START_REF] Abbon | [END_REF]4], and even for muon tomography [5] as used in a radiography of a pyramid [6]. In nuclear physics a MicroMegas-based time-projection-chamber (TPC) for fission fragment tracking (NIFFTE) has been put in operation recently [7,8].

The applicability of MicroMegas detectors for a diverse range of ionizing particles is due to the high range in possible gain, allowing to detect particles with very different energy deposits in the drift region. Therefore the versatility of the detector finds applications in detecting low-energy X-rays and even ultra-violet light in the eV range, to the detection of 100 MeV fission fragments.

While MicroMegas detectors detect ionizing particles, an interesting application is its use as a neutron detector. The key for neutron detection is its conversion into a charged particle, either a light charged particle like a proton, an ↵-particle, or a fission fragment. The application of MicroMegas detectors with neutron beams is not only ⇤ e-mail: gunsing@cea.fr useful at continuous neutron sources, typically as neutron monitors, but can be further extended to the use at pulsed time-of-flight facilities, such as GELINA at JRC-Geel [9], NFS at GANIL, or n_TOF at CERN [10]. For neutron time-of-flight, the timing of the signal is important since it is a direct measure of the incident neutron energy.

MicroMegas stands for micro-mesh gaseous structure and is a parallel plate gaseous detector, composed of two gas volumes separated by a micromesh, which is a conductive electrode with many holes, such that the two gas volumes can be considered one for the gas flow. The first gas region is the drift volume. The ionizing particle crossing the drift zone ionizes the gas and releases primary electrons. It has an electric field which is in the ionization chamber regime, typically 1 kV/cm depending on the gas and the pressure. The field prevents the ions to recombine and the electrons drift to the micromesh, where they undergo in the second gas volume, the amplification region, a much stronger electric field which is in the avalanche or proportional counter regime, typically 100 kV/cm. Here the electrons are multiplied as secondary electrons and this part acts as a parallel-plate avalanche counter. This electronic avalanche considerably amplifies the electrical signal due to the initial energy deposition of the particle. The distance of the amplification region is much smaller than the drift region, typically 50 µm for bulk and microbulk detectors. The electrons are collected at the anode, which often takes the role as readout device and is in many applications implemented as readout pixels, or orthogonal micro-strips in order to reduce the count rate per readout channel, and obtain position information. If position information is not needed, for example when used as a simple counter, the anode can also be implemented as a single pad.

Earlier generation MicroMegas detectors are assembled mechanically. Especially the mesh-anode mounting is a critical step because of the strong forces due to the high electric field which may result in a varying meshanode distance and therefore a inhomogeneous electric field. Such problems are nowadays largely overcome by the use of the bulk technology [11]. The mesh structure and the anode readout strips or pixels are directly integrated in printed circuit board layers. This has resulted in much more robust detector elements. The bulk technique is at present the most widely spread production technique.

An even more recent development is the microbulk technology [12]. The starting point for a microbulk detector is a copper-coated kapton foil. Using optical masks and chemical etching, a mesh structure is created on one side of the foil. Small holes in the copper layer are created and the underlying kapton is removed. The opposite copper layer remains usually as a single surface. The remaining kapton act as spacers between the two copper layers and the gas-filled space between the copper plates is the amplification region. In figure 1 the principle of the Mi-croMegas detector is shown, here for a microbulk detector. Usual thicknesses are 50 µm of kapton and 5 µm copper on each side. Smaller gaps have been tested as well but appeared to produce less e cient avalanches at atmospheric presssure. Microbulk detectors show a very stable gain and excellent energy resolution [13]. The gas is continuously renewed in order to keep a constant ionizability. Figure 2 shows a microscope picture with the hole structure of a microbulk. Very recently, the production process of microbulk has been significantly improved with the use of laser direct imaging (LDI) instead of photolithography. LDI allows for the production of larger size detectors and a reduced interstrip region.

The in-beam material balance of such a detector is very low, most neutrons pass through the detector without interaction. For this reason, such neutron detectors are sometimes called "transparent". Usually the strongest interaction comes from the neutron-to-charged particle converter. For neutron monitoring this is usually 10 B, 6 Li, 235 U, or 238 U. These nuclei have neutron-induced reaction cross sections considered standard so that the number of incident neutrons can be accurately deduced. Also the transmission of neutrons through this material can be correctly determined and taken into account in the calculation of the ratio of the transmitted neutron flux with respect to the incident neutron flux. The three volages are chosen such that the electric fields form the ionization chamber and proportional counter regimes in the drift and amplification region respectively.

Use of MicroMegas with pulsed neutron beams

Unlike charged particle beams which can be focussed with magnets, neutron beams can only be shape through collimation and therefore are used with diameters in the order of typically several centimeters. One of the challenges of accurate measurements of neutron-induced reactions, in particular for neutron capture measurements, is to determine the number of incident neutrons, (fluence or flux measurements), and their spatial distribution (beam profile) as a function of neutron energy deduced via measured time-of-flight. The MicroMegas detectors used with neutron beams can be distinguished in two types: the "single pad" detectors with a single read-out channel, used for neutron-induced reaction measurements, and the segmented detectors with multiple read-out channels, typcially used for neutron imaging, but with the potential to be adapted for cross section measurements, including angular distributions.

neutron reaction detectors

The energy-density of the neutron as a function of neutron energy, shortly called the neutron flux, is an essential quantity to any cross section measurement. Without the need for the absolute number of neutrons, the relative change of the flux with neutron energy is usually the information needed to determined reaction cross sections from time-of-flight measurements. Thin in-beam neutron monitors are therefore the most appropriate detectors for this D R A F T purpose. At the n_TOF facility the use of o↵-beam silicon detectors with in in-beam 6 Li foil has been succesfully used since the start of the facility. Transparent microbulk MicroMegas neutron detectors have been developed for flux measurements at the n_TOF facility alongside other neutron flux detectors [14]. Nevertheless, MicroMegas detectors at n_TOF are usually employed for di↵erent purposes. Three formats of MicroMegas detectors have been developed. One with an active diameter of 35 mm, one with a diameter of 60 mm, used for setups with neutron beams from a small collimator, like for capture measurements, and one with an active diameter of 95 mm, used for setups with a large collimator, typically for fission experiments [15], but also for (n,↵) measurements [16]. Pictures of these three formats are shown in figure 3. The transparency allows to stack several detectors in a single reaction chamber, in this way significantly decreasing the necessary beam time. For fission measurements, a reference sample can be part of the stack of detectors, resulting in very accurate fission ratios. An example of a stack of MicroMegas detectors is shown in figure 4. A variation of this single pad detector has been tested as well, by dividing the anode in four quarters of a circle, with the goal to achieve a quick way to find the beam center. Nevertheless, since the mesh covering the four quarter anodes is a single circle, an event in one quarter induces signals in the other quarters, making the data analysis cumbersome.

neutron beam-profile detectors

The neutron beam profile detectors were until recently implemented as bulk detectors on PCB support. Neutron capture measurements usually consist of a capture sample in a pulsed neutron beam, viewed by gamma-ray detectors outside the beam. This results in a capture gamma-ray spectra as a function of neutron time-of-flight. Such a measurement usually is normalized by a reference sample placed in the same position as the capture sample. The normalization is extracted from the reference sample in a very limited energy range (usually a "saturated" resonance) and then applied to the capture sample over the entire energy range. Therefore it is important to know if the beam profile, or more precisely the fraction of neutrons incident on the sample, changes with neutron energy. In order to measure the energy-dependence of the neutron beam profile, a first MicroMegas detector in the form of a bulk detector with mono-directional anode read-out strips, developed for the CAST experiment [4], has been used at n_TOF [17]. The detector consisted of a segmented anode of 50 strip of 1.5 mm wide and used a 595 nm 6 LiF foil as a neutron converter. By rotating the detector around the axis of the neutron beam, data were taken for 0 , 30 and 90 . From a combined analysis of the data at di↵errent angles the neutron beam profile could be extracted [17]. Within the measurement uncertainties the profile was found to be in agreement with FLUKA simulations in the used energy ranges.

A second beam profile detector, based on a prototype for CAST, had orthogonal X-and Y-strips, 106 in each direction, and was used in 2009 at n_TOF. The energydependent profile was determined from coincidences in the X and Y strips, together with the time-of-flight information. The drift electrode was covered with a 10 B 4 C layer to detect the neutron-induced light charged particles from the 10 B(n,↵) reaction. The data acquisition was based on the Gassiplex multiplexer. The timing information of this device does not allow track reconstruction to find the neutron interaction point. Extensive tests and simulations were performed for this detector. A typical beam image for an energy interval at low neutron energy, taken from ref. [18], is shown in the left panel of figure 1.

The use of such an image is in the first place to identify the absolute position of the neutron beam spot, which depends on the configuration and placement of the collimators. Then for capture measurements, the part of beam that impinges on the capture sample can be determined. This is usually referred to as the beam interception factor. For this it is possible to find an analytical function describing the image, but it is far more easier to integrate the counts in the two-dimensional histogram over the shape of capture sample. Pixellized MicroMegas Bulk detector After this XY MicroMegas detector a pixellized detector, again a prototype from CAST, was used. The detector realized in a PCB, consisted of 308 pixels, disposed with a pitch of 2.5 mm and enveloping a circular shape of 5 cm diameter. The resulting image, shown in the right panel of figure 5, has evidently a much worse resolution because of the larger pixel sizes.

A breakthrough for the strip detectors came with the advent of the possibility to segmentize not only the anode, but also the mesh of microbulk detector. This was the result of a prototype evolution made within an RD51 project. In this way, a real 2D structure was achieved without addition of extra layers, resulting in a very low-mass neutron profiler, practically transparent to neutrons. The very first detector with a transparent stripped microbulk detector was developed with 60+60 strips of 1 mm wide, and was used for measurements at GELINA and then at n_TOF. One side with strips is shown in figure 6. The detector was coupled to a data acquisition system based on the AGET ASIC chip [19]. This system o↵ers the possibility of an auto-trigger mode and records the time difference between the strips recording a signal, allowing for the reconstruction of the track of the charged particles in the detector gas and therefore the interaction point of the incident neutrons. A full description of this detector and results can be found in ref. [20].

Outlook

The new technical possibilities of microbulk MicroMegas detectors with both a segmented anode and mesh, com-bined with high precision LDI patterns, allow in principle for the unification of the transparent single-pad detectors, used for beam monitoring, fission, and (n,↵) or other light charged particle measurements, and the XY-type detectors, used for beam imaging. In addition, the distinct observation of the arrival times induced by a single track, as already observed in ref. [17] and further exploited in ref. [20], may open the possibility of a more precise track reconstruction, in the sense of a simplified time projection chamber (TPC). This may lead to the use of a MicroMegas detector for the measurement of angular distributions of neutron-induced charged particle reactions.

While the GET electronics is very versatile for low count-rate experiments, some shortcomings have been experienced at high count rates. Dedicated electronics, capable of signal sampling with a pace of 1 ns over a repeating 100 ms time window with high local count rates, are essential for time-of-flight experiments. An interesting development in this respect is the VMM3 chip [21] developed for the read-out of the ATLAS-NSW MicroMegas detectors.

DFigure 1 .

 1 Figure 1. The principle of the microbulk MicroMegas detector as a neutron detector. The neutron beam has typcially a diameter of several cm, depending on the used collimators, the detector itself is a bit larger to cover the full neutron beam. The drift electrode is coated with a thin layer of material creating charged particles by neutron-induded reactions. The resulting charged particle ionizes the gas in the drift region. The electrons are multiplied in the amplification region consisting of a chemically etched copper-coated kapton foil. The fast signal is usually read out at either the mesh or the anode.

FrankFigure 2 .

 2 Figure 2. A microscope picture of the mesh of a microbulk detector. The patterns of the holes are clearly visible. The pitch value of 100 µm and the hole diameter of 40 µm are typical for microbulk detectors but may vary between generations and also depend on the kapton thickness and segmentation structure.

Figure 3 .

 3 Figure 3. Three formats of single pad MicroMegas detectors with diamters of 35, 60 and 95 mm, as used in n_TOF experiments.

Figure 4 .

 4 Figure 4. An exampe of a stack of micromegas detectors on a mounting structure for insertion in a reaction chamber.

Figure 5 .

 5 Figure 5. Neutron beam images obtained using a MicroMegas detector with XY strips (left panel). and with a pixellized Mi-croMegas. Figures are from ref. [18].

Figure 6 .

 6 Figure 6. One side of a double sided segmented microbulk, showing the 1 mm wide strips, used for precise neutron beam imaging as function of neutron energy [20].


Discussion

2 Overall turbo encoder structure

Coding rates R ≥ 1/3

The proposed encoder structure uses the same component encoders as in LTE.

Generator polynomials for C1 and C2: (1, (1+D+D 3 )/ (1+D 2 +D 3 ))

Coding rates 1/5 ≤ R < 1/3

If coding rates lower than 1/3 are required, an additional parity is computed for each component convolutional encoder.

Generator polynomials for C1 and C2: (1, (1+D+D 3 )/ (1+D 2 +D 3 ), (1+D+D 2 +D 3 )/ (1+D 2 +D 3 ))

Introduction

The first part of this document (sections 0 to 5) describes the implementation of the enhanced Turbo Coding scheme proposed in R1-164635 at RAN1#85 meeting. The following items are described:

-Component codes -Tail-biting trellis termination technique -Puncturing patterns -Interleaving equations and parameters

The second part of the document (sections 6 and 7) provides the puncturing patterns and the interleaving parameters used to obtain the error rate performance curves presented in R1-164635 (section 6) and in R1-167414 (section 7)

Trellis termination: tail-biting turbo codes

Among the different techniques aiming at transforming a convolutional code into a block code, tailbiting, also called circular encoding, ensures that, when encoding a message of length K, the initial and the final states are identical for each component encoder C1 and C2 [START_REF] Weiss | Code construction and decoding of parallel concatenated tail-biting codes[END_REF].

Tail-biting is the best known termination method for turbo codes:

-First, no extra bits have to be added and transmitted; thus, there is no rate loss and the spectral efficiency of the transmission is not reduced; -Next, tail-biting does not induce any side effect in the message. Consequently, all the information bits are protected in the same way by the turbo code and the circular property prevents the occurrence of low-weight truncated codewords since the trellis can be considered as with infinite length. Therefore, tail-biting termination helps to lower the error floor. Note that the tail-biting technique is not directly applicable when K is a multiple of 7.

-The second step is the actual encoding stage. The encoder starts in the correct initial state Sc and the corresponding valid codeword is delivered.

Tail-biting decoding

When tail-biting is adopted, the code trellis can be viewed as a circle (see figure below): the iterative decoding of such codes involves repeated and continuous turns around the circular trellis. The number of turns performed is equal to the required number of iterations. The state probabilities or metrics, according to the chosen decoding algorithm, computed at the end of each turn are used as initial values for the next turn. For instance, if the MAP, Log-MAP or Max-Log-MAP soft-in soft-out decoding algorithm is used, the final forward (respectively backward) state probabilities or metrics computed at the end of each iteration are used as initial values for the next iteration. The decoding process can start anywhere in the circular trellis. At the first iteration, the forward and backward processes can be initialized with equiprobable values.

Puncturing

Let us denote by K the size of the information message to be encoded.

Puncturing is performed using periodic puncturing patterns of length Q. K is assumed to be a multiple of Q. Typical values for Q are 4, 8, 16 or 32 but others values are possible, provided that Q is a divisor of K.

The selection of the puncturing patterns is performed on the basis of the joint analysis of the Hamming distance spectrum of the punctured component convolutional code and of the mutual information exchange between the two component encoders [START_REF]Improved LTE turbo codes for NR[END_REF].

It was shown that, for a given coding rate, the same puncturing pattern can be used for a large range of information message lengths 𝐾. In practice, two sets of puncturing patterns are needed:

-A set of puncturing patterns for short block lengths (up to a few hundred bits): for short data blocks, only parity bits are punctured, all the systematic bits are transmitted; -A set of puncturing patterns for long block lengths: for medium and long data blocks, parity and systematic bits are punctured.

Coding rates R > 1/3

For each coding rate greater than 1/3, the puncturing pattern consists of two puncturing vectors of length Q: one for systematic bits (X), the second for the parity bits (Y1 and Y2). The same puncturing vector is applied to Y1 and Y2.

Puncturing vectors are binary vectors. "0" values indicate the bits to be punctured (not transmitted) and "1" values indicate the coded bits to be transmitted.

Example:

Coding rates 1/3 > R > 1/5

For each coding rate greater than 1/5 and lower than 1/3, the puncturing pattern consists of three puncturing vectors of length Q: one for systematic bits (X), one for parity bits Y (Y1 and Y2) and one for parity bits W (W1 and W2). The same puncturing vector is applied to Y1 and Y2. The same puncturing vector is applied to W1 and W2.

Non punctured data K = 16 bits 𝐒 is a vector of size Q. 𝑃, 𝑆(0) … 𝑆(𝑄 -1) values depend on 𝐾 and on the coding rate.

Q = 4 Puncturing vector 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1 0 1 1 1
𝛱 is a bijection provided that:

-P and K are mutually prime numbers, -Q is a divisor of K, -the values S(0) … S(Q -1) belong to the Q different congruence classes modulo Q.

Contention-free property

The ARP interleaver is contention-free for every window size 𝑊 of length 𝒒𝑸, provided that 𝒒𝑸 is a divisor of 𝑲, thus allowing a parallelism degree of 𝑞𝑄 to be naturally achievable.

Principle of selection of the interleaver parameters, 𝑺(𝟎) … 𝑺(𝑸 -𝟏) 𝐚𝐧𝐝 𝑷

Selecting the values of parameters 𝑆(0) … 𝑆(𝑄 -1) and 𝑃 involves the following steps, partially described in [START_REF]Improved LTE turbo codes for NR[END_REF]:

-Selection of P: only the values of P ensuring a high minimum span of the regular interleaver (𝛱(𝑖) = 𝑃 × 𝑖 mod 𝐾) are retained; -In the puncturing pattern of length Q, the data positions are sorted according to their protection level; -𝑆(0) … 𝑆(𝑄 -1): the values of these parameters are chosen in a such a way that data positions with a good level of protection in the puncturing pattern are connected with data positions with a poor level of protection. -Only the resulting interleavers with a high minimum span and a high correlation girth are kept and their minimum Hamming distance is evaluated.

This selection process can be applied in different ways:

-To jointly optimize the code performance for each code rate and block length: a set of parameters is then computed for each rate/length combination (method applied to obtain the parameters described in section 7.1); -To design rate-compatible codes: the parameters are optimized for the highest code rate.

The selected set of parameters is valid for all coding rates (method applied to obtain the parameters described in section 7.2).

Puncturing patterns and interleaver parameters used for results presented at RAN1#85 in R1-164635

The puncturing masks and the ARP interleaver parameters for the different coding rates and information frame sizes are listed in the following tables:

1

 1 Tail-biting encodingTail-biting encoding for each component encoder C1 and C2 requires a two-step encoding process illustrated by the following figure: (a) Circular encoding of message "01101101" with C1 or C2, first encoding step: the message is encoded from state 0. The final state is Sk = 5 (b) Circular encoding of message "01101101" with C1 or C2, second -actual -encoding step: the message is encoded from circulation state Sc = 1 and the final state is also Sc = -The first step determines the initial/final

5 . 1

 51 Definition of the interleaving function 𝚷 The systematic bits are interleaved following an Almost Regular Permutation (ARP) process [4]: For 𝑖 = 0 ⋯ 𝐾 -1 𝑗 = 𝛱(𝑖) = [𝑃𝑖 + 𝑆(𝑖 mod 𝑄)] mod 𝐾 Interpretation: the data value at address 𝑖 in the interleaved message comes from address 𝑗 = 𝛱(𝑖) in the non-interleaved message.

Proof:

  𝛱(𝑖 + 𝑞𝑄) -𝛱(𝑖) = 𝑞𝑃𝑄 mod 𝐾. Consequently, if the memory is split into 𝐾 𝑞𝑄 memory banks of size 𝑊 = 𝑞𝑄, the symbols at interleaved addresses 𝑖, 𝑖 + 𝑞𝑄, 𝑖 + 2𝑞𝑄, 𝑖 + 3𝑞𝑄, … , 𝑖 + ( 𝐾 𝑞𝑄 -1)𝑞𝑄, (i.e. the 𝐾 𝑞𝑄 symbols at the same address in the 𝐾 𝑞𝑄 different memory banks) come from the non-interleaved addresses 𝛱(𝑖), (𝛱(𝑖) + 𝑞𝑃𝑄)mod 𝐾, (𝛱(𝑖) + 2𝑞𝑃𝑄)mod 𝐾, (𝛱(𝑖) + 3𝑞𝑃𝑄)mod 𝐾, … , (𝛱(𝑖) + ( 𝐾 𝑞𝑄 -1)𝑞𝑃𝑄) mod 𝐾 , which represent the same address in the 𝐾 𝑞𝑄 different memory banks, provided that 𝑃 and 𝐾 are mutually prime numbers. Example: for information message length 𝐾 = 8000, puncturing mask length 𝑄 = 16, the interleaver structure allows natural parallelism degrees equal to 2, 4, 5, 10, 20, 25, 50, 100, 125, 250, 500 (i. e. for integer values of 𝐾 𝑞𝑄 ).

Puncturing patterns and interleaver parameters used for results presented at RAN1#86 in R1-167414 7.1 Optimized Turbo Code for K = 6000 and K = 8000 A

  joint optimization of the puncturing patterns and of the ARP interleaver parameters has been carried out for two information block lengths, K = 6000 and K = 8000. The following subsections provide the tables describing the proposed puncturing masks and ARP interleaver parameters.

					ARP interleaver parameters
	R	K	Q	P	(𝑆(0) … 𝑆(𝑄 -1))
	1/5 100	4	13	(0, 73, 99, 24)
	2/3	48	8	17	(7, 5, 43, 9, 15, 13, 35, 1)
	4/5	48	16	35	(10, 42, 2, 38, 18, 26, 26, 22, 10, 42, 2, 38, 18, 26, 26, 22)
	8/9	96	16	35	(8, 60, 47, 78, 26, 67, 82, 78, 88, 81, 80, 92, 37, 84, 16, 68)
	2/3 1504 8	651	(0, 89, 528, 852, 1501, 1396, 688, 490)
	4/5 1504 16 365	(0, 1261, 1374, 1279, 417, 867, 549, 514, 730, 474, 1359, 285, 927, 670,
					1176, 1078)
	8/9 1504 16 487 (0, 943, 1030, 1320, 182, 955, 887, 441, 1040, 1452, 625, 364, 1195, 280,
					835, 1363)
	2/3 6144 8	701	(0, 2479, 1115, 5007, 2957, 3489, 4661, 1996)
	4/5 6144 16 953	(0, 801, 3826, 5118, 210, 1698, 6065, 684, 5076, 2695, 4119, 5250, 775,
					3768, 624, 11)
	1/5 8000 16 1507	(8, 3443, 7934, 4420, 7894, 7903, 511, 7397, 2248, 4672, 1481, 3464,
					1675, 3116, 7435, 4735)
	8/9 8000 16 5153	(8, 4709, 3666, 4474, 4686, 1241, 1355, 6499, 952, 6114, 3037, 910,
					3315,
					5718, 7143, 2541)
	7
	R		K		Puncturing vectors : Systematic (X)/ parity (Y1 and Y2)
	2/3		48		11111111 / 10001000
	4/5		48		1111111111111111 / 0100000001000000
	8/9		96		1111111111111111 / 0100000000000000
	2/3	1504, 6144	01111110 / 11000001
	4/5	1504, 6144	0111111111111101 / 1100000000000010
	8/9	1504, 8000	0111111101111111 / 1010000000000000
	Note : "1" means "non-punctured (transmitted) symbol" ad "0" means "punctured (non-
	transmitted) symbol"

7.1.1 Puncturing patterns for K = 6000 and K = 8000 R K Puncturing vectors : Systematic (X)/ parity (Y1 and Y2)

  and ARP interleaver parameters for block length K = 96 and K = 4000. As described in section 4, the puncturing patterns are different for short and long block lengths: for short

	proposed puncturing masks
	2/5	6000, 8000	1111111110111110 / 1011101111101111
	1/2	6000, 8000	1111111100111111 / 1011001111001010
	2/3	6000, 8000	01111110 / 11000001
	3/4	6000, 8004	111111011110 / 010001010000
	5/6	6000, 8000	11111011111101111111 / 10000010000100000000
	8/9	6000, 8000	0111111101111111 / 1010000000000000
		Note : "1" means "non-punctured (transmitted) symbol" ad "0" means "punctured (non-
			transmitted) symbol"

data blocks, only parity bits are punctured, all the systematic bits are transmitted and for medium and long data blocks, parity and systematic bits are punctured. 7.2.1 Puncturing patterns for K = 96

	R	Parity puncturing vectors (Y1 and Y2) for systematic (X) = 1111111111111111
	8/23	1101111111111111
	4/11	1101111111101111
	8/21	1101111101101111
	2/5	1101011101101111
	8/19	1101011101101110
	4/9	1101011101001110
	8/17	1101011100001110
	1/2	1101011100001010
	8/15	1101010100001010
	4/7	1101010000001010
	8/13	1101010000000010
	2/3	1100010000000010
	8/11	1100000000000010
	4/5	0100000000000010
	8/9	0100000000000000
	Note : "1" means "non-punctured (transmitted) symbol" ad "0" means "punctured (non-
		transmitted) symbol"
	7.2.2 Puncturing patterns for K = 4000
	R	Parity puncturing vectors (Y1 and Y2) for systematic (X) = 0111111101111111
	8/23	1111111111111111
	4/11	1110111111111111
	8/21	1010111111111111
	2/5	1010111110111111
	8/19	1010111110111101
	4/9	1010111010111101
	8/17	1010111010110101
	1/2	1010111000110101
	8/15	1010111000110100
	4/7	1010111000110000
	8/13	1010110000110000
	2/3	1010010000110000
	8/11	1010000000110000
	4/5	1010000000010000
	8/9	1010000000000000
	Note : "1" means "non-punctured (transmitted) symbol" ad "0" means "punctured (non-
		transmitted) symbol"


Keywords:

Introduction

A Study on New Radio Access Technology was approved in RAN#71 meeting [START_REF]New SID Proposal: Study on New Radio Access Technology[END_REF]. The channel coding scheme is a fundamental component for fulfilling the different requirements of next generation radio access technologies [START_REF]New Study Item Proposal: Study on Scenarios and Requirements for Next Generation Access Technologies[END_REF]- [START_REF]New SID Proposal: Study on New Radio Access Technology[END_REF]. The current LTE coding schemes have not been designed for the new requirements of the identified usage scenarios such as eMBB (enhanced mobile broadband), mMTC (massive machine type communication), and uRLLC (ultra-reliable low latency communication).

In this contribution, we analyze the strengths and weaknesses of the existing LTE channel coding schemes in relation to the requirements of the new radio interface and we propose a new design of turbo codes that can compensate for the weaknesses of the legacy LTE turbo codes.

Analysis of the channel coding requirements the New Radio Access Technology

Each identified usage scenario has specific requirements related to the channel coding scheme:

-eMBB: for this usage scenario, the channel coding scheme should support a large range of data rates, from very low data rates for instant messages or control signaling to very high data rates (20 Gbps for downlink and 10 Gbps for uplink) [START_REF]Study on Scenarios and Requirements for Next Generation Access Technologies[END_REF] with improved error correction capabilities and at the price of a reasonable implementation cost. The coding scheme should be flexible in terms of data block sizes and coding rates. The different latency requirements for data and control planes should also be satisfied.

-mMTC: the use cases involving a massive distribution of sensors and actuators require the channel coding scheme to support small packets (a few dozen to hundred bits), with energy-efficient encoding and decoding which is necessary for mMTC long-life devices.

-uRLLC: the channel coding scheme must fulfil high reliability on small packets with very low latency.

Analysis of LTE turbo coding scheme

The LTE turbo code presents benefits inherent to the turbo code family:

-High flexibility with respect to data block length and coding rate: a unique code structure can be used for a large range of data block sizes and coding rates. The different coding rates are obtained by puncturing some transmitted data, allowing rate compatibility and incremental redundancy.

-Very good error correction performance at high to medium error rates for a large range of block sizes and coding rates: turbo codes keep very good performance when punctured. It has been repeatedly observed that turbo codes tend to outperform LDPC codes at shorter block lengths and low coding rates. A recent study of channel coding for space mission telecommand links [START_REF] Baldi | Advanced Channel Coding for Space Mission Telecommand Links[END_REF] has shown that coding schemes based on turbo codes can outperform the latest ones based on LDPC codes, especially for short to medium frame sizes. -Implementation maturity and short time-to-market: turbo code implementation is mature and widely used. Continuing to use turbo codes would reduce the design time of the channel coding component.

Combined with the very mature turbo decoder implementation, the time-to-market for the new radio interface would be reduced.

Observation 1: Turbo codes show native flexibility in code rates and frame sizes with a high implementation maturity.

Observation 2: Turbo codes can offer similar and often better performance than LDPC codes especially for short frame sizes.

On the other hand, the LTE turbo code presents some shortcomings that should be addressed in the new radio interface:

-Error floor: a known issue of the LTE TC is its poor performance at low error rates when transmitting data with coding rates higher than 1/3. This is due to the fact that, for some combinations of block size and coding rate, the LTE rate matching module leads to bad interactions between puncturing and interleaving in the turbo encoder structure, entailing early error floors in the error rate curve [START_REF] Cheng | Analysis of circular buffer rate matching for LTE turbo code[END_REF]. This shortcoming can be eliminated by jointly designing and optimizing the turbo code interleaver and the puncturing mechanism in order to avoid these negative interactions. -Trellis termination: tail bits are used to terminate the trellis of the component convolutional codes of the LTE turbo code. Firstly, this results in a non-negligible bandwidth efficiency reduction for short frames. Secondly, this type of trellis termination introduces low-weight truncated codewords and does not ensure the same protection for all data bits, since tail bits are not encoded twice (i.e., turbo encoded) as regular data are, thus contributing to the error floor issue. A more efficient termination technique is the tail-biting technique [START_REF] Weiss | Code construction and decoding of parallel concatenated tail-biting codes[END_REF]. This technique, already applied to the convolutional code used for the downlink channels of Narrow-Band IoT systems in Release 13. Last but not least, circular trellises make it easier for the implementation of parallel turbo decoding using several component decoders.

Observation 3: LTE turbo codes are far from achieving the full potential of turbo codes mainly due to the error floor and trellis termination issues.

Concerning power consumption and hardware complexity, turbo decoders are sometimes considered inferior to other decoder families (e.g. LDPC). However, most evaluations do not compare implementations supporting the same numbers of code rates and block lengths. The particular code rate values are also of great importance. Indeed, LDPC codes are more efficient at very high code rates, whereas turbo codes are best at low to medium code rates [START_REF] Weiss | Code construction and decoding of parallel concatenated tail-biting codes[END_REF]. Complexity assessment greatly depends on the values of the coding rates and the number of possible combinations to implement. Meaningful efficiency metrics are needed to quantify the implementation complexity of a receiver. Most of the current established efficiency metrics are based on counting operations, thus neglecting important issues like data and storage complexity and access [START_REF] Weiss | Code construction and decoding of parallel concatenated tail-biting codes[END_REF].

Regarding high throughput turbo decoders, several implementations providing useful data throughput beyond 1 Gbps were reported in the literature: for instance, [START_REF] Sun | Efficient hardware implementation of a highly-parallel 3GPP LTE/LTE-advance turbo decoder[END_REF] and [START_REF] Ilnseher | A 2.15 GBit/s turbo code decoder for LTE advanced base station applications[END_REF] report VLSI implementations of turbo decoders achieving processing throughputs of respectively 1.28 Gbps and 2.15 Gbps, when decoding the longest frames (6144 bits) supported by LTE. A more recent paper [START_REF] Li | VLSI implementation of fully parallel LTE turbo decoders[END_REF] shows that fully parallel implementations of the LTE turbo decoder allow processing throughputs greater than 20 Gbps to be achieved with a TSMC 65-nm low-power technology.

Observation 4: State-of-the-art comparisons between codes are inaccurate in most cases since they are limited to computational complexity. Memory requirements and number of memory accesses are important parameters to be further considered.

Observation 5: The number of supported code rate / frame size combinations has a large impact on the complexity of some family of codes such as LDPC codes. Observation 6: Very high throughput (>20Gbps) turbo decoder implementations are being proposed in the literature.

Performance of tail-biting turbo codes with jointly optimized interleaving parameters and puncturing patterns

The error performance curves presented in this section have been obtained with regular binary puncturing patterns of length 𝑄 (𝑄 ≤ 16) and an Almost Regular Permutation (ARP) interleaver, already adopted in several standards [11][12].

The interleaving function is given by the following equation:

Π(𝑖) = (𝑃𝑖 + 𝑆(𝑖 mod 𝑄))mod 𝐾
where i denotes the address of the data symbol after interleaving and Π(𝑖) represents its corresponding address before interleaving. P is a positive integer relatively prime to K, K being the block length and the interleaver size. S is a vector containing Q integer values. The values of parameters P and 𝑆(𝑖), 𝑖 = 0 ⋯ 𝑄 -1, are chosen to support the different block sizes and coding rates.

It was shown in [START_REF] Garzon Bohorquez | On the equivalence of interleavers for turbo codes[END_REF] that the QPP interleavers of the LTE turbo code can be seen as a particular case of ARP interleavers, in which the values of the periodic shifts follow the quadratic term of the QPP interleaver function. Figure 1, Figure 2 and Figure 3 show the performance comparison of the LTE turbo code with a new designed turbo code including tail-biting termination and joint optimization of the interleaver and puncturing pattern, for 3 different LTE block sizes and various coding rates, in AWGN channel.

Figure 4 and5 show the performance of the improved turbo code for two new block sizes (K = 100 and 8000) and coding rates 1/5 and 8/9 (extreme frame sizes and code rate values). In these figures, the obtained error rate performance for the improved TC is given as an example and can be subject to further improvement. The introduced modifications to the existing LTE TC for coding rates higher than 1/3 are minimal since they are limited to the trellis termination, puncturing and interleaving. These modifications have negligible (almost inexistent) impact on hardware complexity. For coding rates lower than 1/3 (e.g. 1/5), each component convolutional code provides two parity bits instead of one. The figures show that BLock Error Rates (BLER) down to 10 -6 or lower can be achieved without significant change of the curve slope in all the simulated cases. For short frame sizes, performance gains can reach up to several dBs for high coding rates. 1.E-10

1.E-09

1.E-08

1.E-07

1.E-06

1.E-05

1.E-04

1.E-03

1.E-02

Conclusion

Legacy turbo codes are far from achieving their full potential due to non-optimized interleaver and puncturing schemes as well as trellis termination. The error floor can be significantly lowered thanks to the joint optimization of the interleaver and puncturing schemes as demonstrated by our Monte Carlo simulations. A new design of turbo code is perfectly fitted to fulfil the requirements of NR with a time to market advantage inherited from the legacy LTE turbo codes.

Observations and proposals

Observation 1: Turbo codes show native flexibility in code rates and frame sizes with a high implementation maturity.

Observation 2: Turbo codes can offer similar and often better performance than LDPC codes especially for short frame sizes.

Observation 3: LTE Turbo codes are far from achieving the full potential of Turbo codes mainly due to the error floor and trellis termination issues. Observation 4: State-of-the-art comparisons between codes are inaccurate in most cases since they are limited to computational complexity. Memory requirements and number of memory accesses are important parameters to be further considered.

Observation 5:

The number of supported code rate / frame size combinations has a large impact on the complexity of some family of codes such as LDPC codes.

Observation 6: Very high throughput (>20Gbps) turbo decoder implementations are being proposed in the literature.

Proposal 1: Use tail-biting for trellis termination Proposal 2: Completely re-design the puncturing and interleaving scheme of turbo codes in order to fulfil the tight requirements of NR

Figure 1 .

 1 Figure 1. Performance comparison of the improved turbo code with the LTE turbo code in AWGN channel for coding rates 2/3 and 4/5 in terms of BLock Error Rate vs Eb/N0. BPSK modulation, block size K = 48 bits, 8 decoding iterations.

Figure 2 .

 2 Figure 2. Performance comparison of the improved turbo code with the LTE turbo code in AWGN channel for coding rates 2/3, 4/5 and 8/9 in terms of BLock Error Rate vs Eb/N0. BPSK modulation, block size K = 1504 bits, 8 decoding iterations.

Figure 4 .

 4 Figure 4. BLock Error Rate performance of the improved turbo code in AWGN channel for coding rates 1/5 (K = 100) and 8/9 (K = 96). BPSK modulation, 8 decoding iterations. Comparison with LTE turbo code (K = 96).

Figure 5 ./5 and 8 / 9 .

 589 Figure 5. Block Error Rate performance of the improved turbo code in AWGN channel for coding rates 1/5 and 8/9. BPSK modulation, block size K = 8000 bits, 8 decoding iterations.

Performance comparison of the improved turbo code with the LTE turbo code in AWGN channel for coding rates 2/3 and 4/5 in terms of BLock Error Rate vs Eb/N0. BPSK modulation, block size K = 6144 bits, 8 decoding iterations.

	1.E+00 1.E+00
																	LTE TC LTE TC
		1.E-01															Enhanced TC Enhanced TC
	1.E-01															R=2/3 R=2/3
																	R=4/5 R=4/5
	1.E-02
	1.E-03
	BLER 1.E-04 BLER
	1.E-05
	1.E-06
	Figure 3. 1.E-07	0 0.5	1	2 1	3	4 1.5	5	2	6	7 Eb/N0 (dB) 8 2.5 Eb/N0 (dB)	9	3	10	11 3.5	12	13 4	14	15 4.5
	1.E+00
	1.E+00															LTE TC Enhanced TC LTE TC (k=96)
		1.E-01 1.E-01															R=2/3 Enhanced TC
																	R=4/5 R=1/5
																	R=8/9 R=8/9
		1.E-02 1.E-02
		1.E-03 1.E-03
	BLER BLER	1.E-04 1.E-04
		1.E-05
		1.E-05
		1.E-06
		1.E-06
		1.E-07
		1.E-07
		1.E-08	0		1		2		3		4		5		6		7		8
			-1	0	1	2	3	4		5	6 Eb/N0 (dB) 7 Eb/N0 (dB)	8		9	10	11	12	13	14


Observation 2: Improved Turbo code tends to outperform proposed LDPC code when decreasing frame sizes. Observation 3: Performance gain of the improved Turbo code can exceed 1.5dB for 100-bit frame size. Observation 4: The observed gain of the improved Turbo code increases with the coding rate. Observation 5: No error floor was observed for error rates as low as 10 -6 of BLER for the improved Turbo code.

Introduction

Simulation results for the different coding schemes have been presented during the last two RAN1 meetings. However, direct comparisons of obtained results by different proponents have not been performed yet. Indeed, due to the lack of agreement regarding strict constraints on simulation conditions and due the small differences obtained in most performance results, it is quite difficult to derive concrete conclusions. In fact, most of the performance differences result from the disparities in the simulation conditions such as the number of iterations and the choice of the decoding algorithm. Therefore, there was a common informal understanding that the different code proposals are all equivalent from the performance point of view.

In this contribution, we analyze some of the results obtained for the short frame sizes where large differences exist between the different code families. These differences are beyond the gaps that can be observed due to unfair simulation conditions.

Performance comparison

The performance comparison presented in this section focuses on comparing the results of the contributions for the LDPC codes [START_REF]LDPC -Performance evaluation[END_REF] and for the improved Turbo code [START_REF]Enhanced Turbo Codes for NR: Performance Evaluation[END_REF]. Please note that the simulation conditions seem "unequal", favoring the LDPC code family since the best decoding algorithm based on the sum-product method is used with as high as 50 iterations.

Indeed in practice, a simplified version of the log-domain variant is commonly used known as "offset minsum" which generally presents a slight degradation in performance of several tenths of a dB with respect to the sum-product version. In most cases, this penalty increases with decreasing coding rate calling for other more complex variants based on the -min algorithm [START_REF] Guilloud | Lambda-Min decoding algorithm of regular and irregular LDPC codes[END_REF]. In addition, 50 decoding iterations can be considered as excessive in practice and in comparison to the 8 iterations performed for the turbo decoder despite the unequal complexity of the iteration for each type of decoder family.

We recall the simulation conditions: The simulations were performed over an Additive White Gaussian (AWGN) channel and a QPSK modulation.

For the LDPC decoder [START_REF]LDPC -Performance evaluation[END_REF] denoted by Multi-Edge (ME) LDPC in Fig. 1: -Sum-product algorithm -Floating point simulations -50 iterations For the Turbo decoder [START_REF]Enhanced Turbo Codes for NR: Performance Evaluation[END_REF] denoted by Enhanced TC in Fig. 1: -Max-Log MAP algorithm with a scaling factor (simplified log-domain algorithm) -Floating point simulations -8 iterations After analyzing the simulation results in the previously mentioned contributions, we can state that the conclusions indicating "similar" performance indeed holds for larger frame sizes since the observed performance differences are within the margins caused by the unequal simulation conditions. Of course, the compared codes do not achieve such results at the same hardware complexity. Comparisons regarding complexity are not addressed in this contribution. Furthermore, some tendencies can be observed. Turbo codes tend to outperform LDPC codes when decreasing the frame size despite the simulation conditions favoring the LDPC code. Indeed, for short frame sizes of around 100 information bits, we can clearly see in Fig. 1 that the proposed improved turbo code largely outperforms the proposed LDPC code by more than 1.5dB in some cases. It is important to note that the gap increases with increasing coding rate in favor of the turbo code while it is commonly assumed that such a code family presents a weakness for such high rates.

Another interesting aspect is the absence of the error floor down to 10 -6 of BLER for the improved turbo code.

Observation 1: The improved Turbo code and the proposed LDPC code present similar performance at large frame sizes.

Figure 1 .

 1 Figure 1. Performance comparison of the improved turbo code with the LDPC code in AWGN channel for coding rates ranging from 1/5 to 8/9 in terms of BLock Error Rate vs Es/N0. QPSK modulation, block size K around 100 bits.


Introduction

This document describes the error rate performance of the enhanced Turbo Coding scheme proposed in R1-164635 at RAN1#85 meeting and detailed in R1-167413.

The simulation conditions of the decoding process are the following:

-Max-Log-MAP decoding of codes C1 and C2 with application of scaling factors to extrinsics: 0.6 for the first decoding iteration, 1.0 for the last decoding iteration, 0.7 for the other iterations; a short training is used for having an estimate of forward and backward recursions at trellis edges only at first iteration. -Floating-point representation of the LLR (Log-Likelihood Ratio) values; -8 decoding iterations (1 iteration = decoding of code C1 + decoding of code C2); -AWGN and fast fading Rayleigh transmission channel; -QPSK, 16QAM and 64QAM modulations; -The lowest points in the curves were obtained with at least 50 erroneous blocks.

Interleaver and puncturing parameters

The proposed enhanced Turbo code represents a rate compatible design where the same interleaver parameters are kept for all the considered coding rates. Therefore, only the puncturing is varied from one coding rate to the other. In addition, the puncturing is incremental with the coding rate. In other words, the puncturing for a higher coding rate is the same as the one with the lower rate with an additional punctured position. Therefore, incremental redundancy is natively supported between all proposed puncturing schemes. In addition, the extension to one-bit codeword granularity can be easily supported with a guarantee on stable performance.

Almost Regular Permutation (interleaver design)

The interleaving function is detailed in R1-167413 and given by the following equation:

       mod mod i Pi S i Q K (1.1)
where i denotes the address of the data symbol after interleaving and

 

 i represents its corresponding address before interleaving. 0100000000000000 Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

eMBB scenario

Puncturing mask R=1/5

Two possibilities can be used: First possibility: constituent code RSC(1, 15/13, 17/13)8 there is no puncturing.

Second possibility: constituent code RSC(1, 15/13, 17/13, 11/13) 8 the puncturing mask is: Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

Systematic
The second possibility exhibits better performance by around 0.4 dB at 10 -4 of BLER. The same ARP parameters are used for all coding rates of a particular frame size K. Therefore, incrementally moving from any high coding rate to any lower rate is possible by transmitting only corresponding parity bits from the puncturing mask. These puncturing masks apply for the 4 different frame sizes.

ARP interleaver parameters for K=96 bits ARP interleaver parameters (K=96)

Q P        0 ...

URLLC and control channel scenarios

The interleaver parameters designed for block sizes of eMBB (K= 96, K=208, K=400 and K=992 bits) can be reused for URLLC and control channel scenarios down to coding rate R = 1/5 with puncturing masks provided for eMBB. Then, for coding rates R < 1/5, puncturing masks and polynomials used for URLLC and control channel provided next are applied.

Puncturing masks for Rates R ≥ 1/3

These masks apply only for sizes specific for URLLC (K=32 and K=80 bits). For R=1/3 the considered constituent code is RSC(1, 15/13)8 there is no puncturing.

R

Parity puncturing mask for systematic = 1111 1/2 1010 2/3 1000 Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

Puncturing mask R=1/6

Considered constituent code RSC(1, 15/13, 17/13, 11/13) 8 the puncturing mask is:

Systematic 0000 Parity (FF=15)
1111 Parity (FF=17) 1111 Parity (FF=11) 1111 Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

Puncturing mask R=1/8

Considered constituent code RSC(1, 15/13, 17/13, 11/13, 16/13) 8 the puncturing mask is: Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

Systematic

Puncturing mask R=1/10

Considered constituent code RSC(1, 15/13, 17/13, 11/13, 16/13, 12/13) 8 the puncturing mask is: Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

Systematic

Puncturing mask R=1/12

Considered constituent code RSC(1, 15/13, 17/13, 11/13, 16/13, 12/13, 17/13) 8 the puncturing mask is: Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

ARP interleaver parameters for K=32 bits ARP interleaver parameters (K=32)

Q P        0 ... 1 S S Q 4 9 (3, 5, 3, 5) 2.3
       0 ... 1 S S Q 4 11 (3, 63, 3, 63)
The same ARP parameters are used for coding rates 2/3, 1/2, 1/3, 1/6, 1/8, 1/10 and 1/12 of a particular frame size K.

Performance results

The performance results presented in section 3 were obtained using the puncturing patterns and the interleaving parameters described in the previous sections. We start by QPSK constellation. Then 16QAM and 64QAM simulations are provided followed by some results over Rayleigh fading channel.

1.E-04

1.E-03

1.E-02

1.E-01

List-like decoding

List decoding can also be performed on Turbo codes. Large improvements can be achieved, greatly approaching Maximum Likelihood (ML) performance. As provided in [START_REF] Helmling | Database of Channel Codes and ML Simulation Results[END_REF], Polar codes benefit largely from list32 decoding for short frame sizes. This can be clearly seen in Figure 21. We can clearly see that list32 performance reaches quasi-ML performance for Polar codes. Similarly, performance evaluations were performed for ML performance for Turbo codes in [START_REF] Helmling | Database of Channel Codes and ML Simulation Results[END_REF]. Results indicate an additional gain from going from Log-Map decoding to ML ranging from 0.5 to 0.9 dB. An example of these results is provided in Figure 22. There could be clear additional gains when applying Quasi-ML decoding for Turbo codes.

Ordered Statistics Decoding with the help of an outer CRC can also be performed for turbo codes as proposed in [START_REF] Wei | A CRC-Aided Hybrid Decoding Algorithm for Turbo Codes[END_REF]. Hardware implementation was also provided for short frame sizes. Gains of more than 2dB were achieved for such solutions indicating the potential of such schemes as shown in Figure 23.

Both of these decoding techniques were also mentioned in [START_REF]WF on channel coding observations for short block size[END_REF]. Simplified or reduced complexity List decoding can also be performed for Turbo codes. Indeed, these techniques can be applied to component convolutional decoders at the price of a reduced complexity since a large number of the performed computations can be shared with the classical Max-log MAP decoding. References and details are provided in Accelercomm's contribution [START_REF]BLER performance of list decoding for enhanced turbo codes[END_REF] on the subject. Large gains can also be obtained in this case at the price of a reduced complexity.

Properties of the ARP interleaver

It has been shown in [START_REF] Berrou | Designing good permutations for turbo codes: towards a single model[END_REF] that ARP interleavers have a degree of parallel processing pQ dividing K, where Q is the ARP period also dividing K and p any integer. In other words, ARP interleavers are contention free for any multiple of the ARP period. Later, it has been mentioned in [START_REF] Takeshita | On maximum contention-free interleavers and permutation polynomials over integer rings[END_REF] that "we believe many ARP interleavers (if not all) are Maximum Contention Free (MCF) and therefore ARP interleavers are stronger with respect to the degree of parallel processing than what is stated in [START_REF] Berrou | Designing good permutations for turbo codes: towards a single model[END_REF]".

The proposed enhanced Turbo code follows a Rate-compatible version of the general guidelines for the ARP model and interleaver design detailed in [START_REF] Garzón-Bohórquez | Improving Turbo Codes for 5G with parity puncture-constrained interleavers[END_REF]. This design ensures periodic connectivity inside the ARP period between a position in the natural order and another in the interleaved order among the possible Q positions. Thanks to this feature, this type of interleaving can be easily shown to be MCF.

Conclusion

Observation 1: Enhanced Turbo codes can greatly improve the performance of LTE turbo codes.

Observation 2: Enhanced Turbo codes can greatly improve the performance with respect to LDPC, especially for short frame sizes.

Observation 3: Quasi-ML or List-like decoding can improve the performance of Turbo codes up to 0.9dB on AWGN channels. Larger gains can be obtained over fast fading channels.

Observation 4: Ordered statistics decoding with Hybrid decoding of Turbo and CRC codes can provide gains of up to 2 dB for short frame sizes.

Observation 5: Several reduced complexity list decoding algorithms for turbo codes exist. They contribute to largely reducing the complexity while improving performance for short frame sizes.

Observation 6: Proposed ARP interleaver is maximum contention free eliminating memory access conflicts for all possible sub-block parallelism.

7 References

Figure 5 :

 5 Figure 5: Performance evaluation of the enhanced turbo code in AWGN channel in terms of BLock Error Rate vs Es/N0. QPSK modulation, information block size K = 208 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination. eMBB, URLLC and control channel Scenarios.

Figure 15 :

 15 Figure 15: Performance evaluation of the enhanced turbo code in Rayleigh fading channel in terms of BLock Error Rate vs Es/N0. QPSK modulation, information block size K = 32 bits, 8 decoding iterations of the Maxlog-MAP algorithm, tail-biting termination.

Figure 16 :

 16 Figure 16: Performance evaluation of the enhanced turbo code in Rayleigh fading channel in terms of BLock Error Rate vs Es/N0. QPSK modulation, information block size K = 80 bits, 8 decoding iterations of the Maxlog-MAP algorithm, tail-biting termination.

Figure 21 :

 21 Figure 21: Performance comparison of a polar code with list32 decoding and ML decoding over AWGN channel in terms of BLock Error Rate vs Eb/N0. QPSK modulation, for several information block sizes. Fig. courtesy of [1].

Figure 22 :

 22 Figure 22: Performance comparison of the LTE turbo code with Log-Map decoding and ML decoding over AWGN channel in terms of BLock Error Rate vs Es/N0. QPSK modulation, several information block sizes, 8 decoding iterations of the Log-MAP algorithm. Fig. courtesy of [1].

Figure 23 :

 23 Figure 23: Performance comparison of the LTE turbo code with OSD and outer CRC over AWGN channel. Information frame size K=40 bits. Fig. courtesy of [2].

2.2.4 ARP interleaver parameters for K=208 bits ARP interleaver parameters (K=208) Q P

			S	   0 ... S Q		1		
	16 147	(8, 156, 31, 174, 10, 115, 98, 62, 152, 97, 16, 156, 37, 84, 112, 68)
	2.2
			S	S Q		1
	16 37	(8, 26, 59, 72, 66, 57, 38, 32, 72, 79, 60, 38, 13, 10, 52, 54)

.5 ARP interleaver parameters for K=400 bits ARP interleaver parameters (K=400) Q P

			S	   0 ... S	Q		1		
	16 383	(8, 80, 311, 394, 58, 55, 250, 298, 56, 197, 280, 40, 229, 40, 136, 192)
	2.2

.6 ARP interleaver parameters for K=992 bits ARP interleaver parameters (K=992) Q P

			S	   0 ... S	Q		1		
	16	(8, 390, 691, 60, 514, 53, 110, 244, 696, 427, 596, 10, 797, 742, 364,
	729			410)

.7 ARP interleaver parameters for K=48 bits

			ARP interleaver parameters (K=48)
	Q	P		S	   0 ... S Q		1		
	4	11		(3, 27, 47, 23)
	2.3.8

ARP interleaver parameters for K=80 bits ARP interleaver parameters (K=80) Q P

  Figure 19: Performance evaluation of the enhanced turbo code in Rayleigh fading channel in terms of BLock Error Rate vs Es/N0. QPSK modulation, information block size K = 400 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination.Figure 20: Performance evaluation of the enhanced turbo code in Rayleigh fading channel in terms of BLock Error Rate vs Es/N0. QPSK modulation, information block size K = 992 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination.

	1.E+00
																						R=1/5
																						R=1/3
																						R=2/5
		1.E-01																				R=1/2 R=2/3
																						R=8/9
	BLER	1.E-02
		1.E-03
		1.E-04
			-6	-4		-2	0		2		4	6		8		10	12		14	16	18	20
											Es/N0 (dB)
	1.E+00
																						R=1/5
																						R=1/3
																						R=2/5
																						R=1/2
	1.E-01																				R=2/3
																						R=8/9
	1.E-02
	BLER
	1.E-03
	1.E-04
		-5	-4	-3	-2	-1	0	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17
												Es/N0	(dB)


Introduction

This document describes the error rate performance of the enhanced Turbo Coding scheme proposed in R1-164635 at RAN1#85 meeting and detailed in R1-167413.

The simulation conditions of the decoding process are the following:

-Max-Log-MAP decoding of codes C1 and C2 with application of scaling factors to extrinsics: 0.6 for the first decoding iteration, 1.0 for the last decoding iteration, 0.7 for the other iterations; a short training is used for having an estimate of forward and backward recursions at trellis edges only at first iteration. -Floating-point representation of the LLR (Log-Likelihood Ratio) values; -8 decoding iterations (1 iteration = decoding of code C1 + decoding of code C2); -AWGN transmission channel; -QPSK and 16QAM modulations; -The lowest points in the curves were obtained with at least 50 erroneous blocks.

Interleaver and puncturing parameters

The proposed enhanced Turbo code represents a rate compatible design where the same interleaver parameters are kept for all the considered coding rates. Therefore, only the puncturing is varied from one coding rate to the other. In addition, the puncturing is incremental with the coding rate. In other words, the puncturing for a higher coding rate is the same as the one with the lower rate with an additional punctured position. Therefore, incremental redundancy is natively supported between all proposed puncturing schemes. In addition, the extension to one-bit codeword granularity can be easily supported with a guarantee on stable performance.

Almost Regular Permutation (interleaver design)

The interleaving function is detailed in R1-167413 and given by the following equation:

       mod mod i Pi S i Q K (1.1)
where i denotes the address of the data symbol after interleaving and    i represents its corresponding address before interleaving.

The same ARP parameters are used for all coding rates of a particular frame size K. Therefore, incrementally moving from any high coding rate to any lower rate is possible by transmitting only corresponding parity bits from the puncturing mask. These puncturing masks apply for all of the different frame sizes.

URLLC scenario

Simulation assumptions: URLLC and mMTC

The agreements for simulation conditions:

 Evaluate BLER performance versus SNR.

 BLER simulations down to 10 -4 are recommended (to observe the error floor) for URLLC.

Channel The interleaver parameters designed for block sizes of eMBB (K= 96, K=208, K=400 and K=992 bits) provided in R1-1613029 proposed at RAN1#87 can be reused for the URLLC scenario down to coding rate R = 1/5 with puncturing masks provided for eMBB. Then, for coding rates R < 1/5, puncturing masks and polynomials used for URLLC provided next are applied.

Puncturing masks

Puncturing masks for Rates R ≥ 1/3

These masks apply only for sizes specific for URLLC (K=20, K=32, K=40, K=48, K=80 bits, K=600 bits). For R=1/3 the considered constituent code is RSC(1, 15/13)8 there is no puncturing.

R

Parity puncturing mask for systematic = 1111 1/2 1010 2/3 1000 Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

Puncturing mask R=1/6

Considered constituent code RSC(1, 15/13, 17/13, 11/13) 8 the puncturing mask is:

Systematic 0000 Parity (FF=15) 1111 Parity (FF=17)
1111 Parity (FF=11) 1111 Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

Puncturing mask R=1/8

Considered constituent code RSC(1, 15/13, 17/13, 11/13, 16/13) 8 the puncturing mask is: Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

Systematic

Puncturing mask R=1/10

Considered constituent code RSC(1, 15/13, 17/13, 11/13, 16/13, 12/13) 8 the puncturing mask is: Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol".

Systematic

Puncturing mask R=1/12

Considered constituent code RSC(1, 15/13, 17/13, 11/13, 16/13, 12/13, 17/13) 8 the puncturing mask is: Note : "1" means "non-punctured (transmitted) symbol" and "0" means "punctured (nontransmitted) symbol". The same ARP parameters are used for coding rates 2/3, 1/2, 1/3, 1/6, 1/8, 1/10 and 1/12 of a particular frame size K.

Interleaver parameters

ARP interleaver parameters for K=20 bits ARP interleaver parameters (K=20)

Q P        0 ... 1 S S Q 4 7 (3,

Performance results

The performance results presented in section 4 were obtained using the puncturing patterns and the interleaving parameters described in the previous sections. We start by QPSK constellation. Then 16QAM simulations are provided over an AWGN channel. 1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

BLER

Es/N0 (dB)

Conclusion

Observation 1: Enhanced Turbo codes can greatly improve the performance of LTE turbo codes especially for the URLLC scenario.

Observation 2: Proposed ARP interleaver is maximum contention free eliminating memory access conflicts for all possible sub-block parallelism.

Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 :Figure 6 :Figure 7 :

 1234567 Figure 1: Performance evaluation of the enhanced turbo code in AWGN channel in terms of BLock Error Rate vs Es/N0. QPSK modulation, information block size K = 20 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination.

.3 ARP interleaver parameters for K=40 bits ARP interleaver parameters (K=40) Q P

	3.3.5 ARP interleaver parameters for K=80 bits
			ARP interleaver parameters (K=80)
	Q	P		S	   0 ... S Q		1		
	4	11		(3, 63, 3, 63)
	3.3.6 ARP interleaver parameters for K=600 bits
			ARP interleaver parameters (K=600)
	Q	P		S	   0 ... S	Q		1		
	4	31	(3, 63, 475, 299)
					3, 11, 15)
	3.3.2 ARP interleaver parameters for K=32 bits
			ARP interleaver parameters (K=32)
	Q	P		S	   0 ... S	Q		1		
	4	9			(3, 5, 3, 5)
	3.3    0 ... S S	Q		1		
	4	11		(3, 19, 31, 7)
	3.3.4 ARP interleaver parameters for K=48 bits
			ARP interleaver parameters (K=48)
	Q	P		S	   0 ... S	Q		1		
	4	11		(3, 27, 47, 23)

  Figure 8: Performance evaluation of the enhanced turbo code in AWGN channel in terms of BLock Error Rate vs Es/N0. 16QAM modulation, information block size K = 20 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination.Figure 9: Performance evaluation of the enhanced turbo code in AWGN channel in terms of BLock Error Rate vs Es/N0. 16QAM modulation, information block size K = 32 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination.Figure 10: Performance evaluation of the enhanced turbo code in AWGN channel in terms of BLock Error Rate vs Es/N0. 16QAM modulation, information block size K = 40 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination.Figure 13: Performance evaluation of the enhanced turbo code in AWGN channel in terms of BLock Error Rate vs Es/N0. 16QAM modulation, information block size K = 600 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination.Figure 14: Performance evaluation of the enhanced turbo code in AWGN channel in terms of BLock Error Rate vs Es/N0. 16QAM modulation, information block size K = 992 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination.

	1.E+00 1.E+00 1.E+00
																								R=1/12 R=1/12 R=1/12 R=1/12
	1.E-01 1.E-01 1.E-01																						R=1/6 R=1/3 R=1/2 R=2/3 R=1/6 R=1/6 R=1/6 R=1/3 R=2/3 R=1/2 R=1/3 R=1/3
	1.E-02 1.E-02 1.E-02 BLER BLER BLER
	1.E-03 1.E-03 1.E-03
	1.E-04 1.E-04 1.E-04
		-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Es/N0 (dB) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 -5 -4 -3 -2 -1 0 1 2 3 4 5 Es/N0 (dB) Es/N0 (dB)	6
	1.E+00 1.E+00 1.E+00
																								R=1/12 R=1/12
																									R=1/12
																								R=1/6
																									R=1/6
																									R=1/6
																								R=1/3
																									R=1/3
																									R=1/3
																									R=1/2
		1.E-01 1.E-01 1.E-01
																									R=2/3
	BLER BLER	1.E-02 1.E-02 BLER 1.E-02
		1.E-03
		1.E-03 1.E-03
		1.E-04
		1.E-04 1.E-04
		-6	-5		-4	-3	-2	-1	0	1	2		3		4	5	6		7	8		9	10	11	12
		-7 -6	-6	-5	-5	-4	-4	-3 -3	-2 -2		-1 -1	0	0	1	2 1	3 2	4	3	5	4	6	5	7	8 6	9	7
													Es/N0	(dB)
												Es/N0 (dB) Es/N0 (dB)

Figure 11: Performance evaluation of the enhanced turbo code in AWGN channel in terms of BLock Error Rate vs Es/N0. 16QAM modulation, information block size K = 208 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination.

Figure 12: Performance evaluation of the enhanced turbo code in AWGN channel in terms of BLock Error Rate vs Es/N0. 16QAM modulation, information block size K = 400 bits, 8 decoding iterations of the Max-log-MAP algorithm, tail-biting termination.