Veronika Bolshakova
email: bolshakova@crai.archi.fr

Gilles Halin

Franck Annie Guerriero

Franck Besançon

Collaboration support for 3D and 4D models: A pedagogical experiment with wooden construction

Keywords: Synchronous collaboration, Pedagogical experiment, CSCW, Decision-making with 3D and 4D, NUI

come

Digital collaboration

Team meetings and collective decision-making (DM) have always been a part of construction project development, where multidisciplinary cooperation requires a significant effort from project stakeholders [START_REF] Staub-French | 3D and 4D modeling for design and construction coordination: issues and lessons learned[END_REF]. For several decades, project development has used digital tools and Building Information Model (BIM) as common instruments [START_REF] Kensek | Building Information Modeling (First edit)[END_REF]. Project teams use BIM as an information source for DM, thus they need an efficient digital collaboration environment [START_REF] Achten | Requirements for Collaborative Design in Architecture[END_REF], with quality interactions [START_REF] Tory | Physical and digital artifact-mediated coordination in building design[END_REF].

Professionals and academia continue their research for better ways to collaborate and to manage projects more efficiently [START_REF] Oxman | Digital architecture as a challenge for design pedagogy: theory, knowledge, models and medium[END_REF]. Following this global dynamic, pedagogical experimentation needs to progress in step with the industry [START_REF] Pikas | Building Information Modeling Education for Construction Engineering and Management. I: Industry Requirements, State of the Art, and Gap Analysis[END_REF]. Academia is well positioned to develop new methods of innovation, knowledge growth and transmission of practices, in addition, it provides a good context for experiments.

Template

This paper summarizes a pedagogical experiment on synchronous collective decision-making with a digital support for visualization and project documents interactions: a multi-touch table with the collaboration software "Shariiing"1 by Immersion2 . This paper is a part of an international research project 4D Collab3 . Project team is composed of research partners and industry partners (including Immersion). The project aims to the design a new collaborative 4D-based decision-making support.

The section 2 of the paper overviews the pedagogical context of experiment, provides specifications for the Digital Collaboration Table (DCT) and describes Digital Collaboration Sessions. It concludes with a description of the experiment feedback collection methods. The next section presents main findings on DCT usability scores by different user categories, and their suggestions for the collaboration support improvements. Finally, the feedback results are emphasized in discussion section, and followed by experiment conclusion and future perspectives section.

Overview of the experiment context and methods

Main experiment steps

The digital collaboration pedagogical experiment (the experiment) introduced a digital support for weekly meetings on project progress. Such support has to offer a homogenous interface for all project documents to avoid software switching. Also, it must offer democratic interactions, such as used in natural user interfaces, along with ease of learning for participants as well.

The experiment had two Phases, the Phase 1 in 2018 and the 2 in 2019 (Fig. 1). The Phase 1 of the experiment was conducted for the Wood Challenge4 (Section 2.2) exercise in 2018, the Step 1 was Wood Challenge, design and construction phases, and Step 2 was collection of the users feedback and the adjustments to the collaboration sessions (Section 2.3). The feedback showed the utility of digital collaboration technology and suggested ways for next year improvements. In Phase 2, as Step 0, with the aim of training all the students to be efficient with a digital collaboration table during the upcoming Wood Challenge 2019, the table was introduced to them in the 1 st semester for a Design Project. Steps 1, 2 have followed to conclude the 2 nd phase of the experiment. Figure 1 illustrates the main steps.

The pedagogical experiment results will contribute, together with professionals' collaboration experiments (not covered by this paper), to design with 4D Collab a new collaboration tool.

Pedagogical exercise: 'Wood Challenge'

Every year, at ENSTIB5 Engineering School of Wood Technologies and Industry, the "Architecture, Wood, Construction"6 postgraduate program launches a pedagogical design and construction exercise called "Wood Challenge"7 . The challenge's main tasks are to design and then build, in teams, a small project with a wooden structure (Fig. 2). Hence, it encourages students to foresee possible problems with their design choices, and to anticipate the answers to construction problems.

Template

The students work in multidisciplinary teams, comprising of an architect, a wood structural engineer and a civil engineer. Also, every team has two additional members: a wood construction professional and an exchange student in architecture or engineering. The diversity of the team emphasizes the importance of efficient communication and collaboration to the students.

All teams work on a defined project type, which varies every year with the same deadline and technical requirements (quantity of materials, structural elements, tools, etc.). Once the design and preconstruction preparations have been completed (6-7 weeks in the beginning of the winter semester), the teams then proceed to construction (1 week in May). The projects are fabricated and assembled on campus. They must not exceed a surface of 15m 2 and a height of 3.8m, and have no more than 10 disassembled modules or elements in order to fit into a truck for transportation to the project installation site. The restricted construction time and added competition element fosters students' abilities to foresee many construction organizational aspects and see optimization for the project design and construction.

Description of the Digital Collaboration Table

Teachers and students weekly gathered around a digital collaboration table (DCT) for project review meetings. The DCT's main element is a multi-touch screen (46" HD, infra-red touch recognition frame), which is embedded in a wooden table frame (Fig. 3). The screen is connected to a PC running "Shariiing" software, a multiuser collaboration environment by "Immersion". The use of the environment at project meetings allows: 1) to visualize construction project documents (plans, sections, 3D models, schedules, quantifications, etc.), 2) to share the same view even being on different sides of the table 3) to manipulate the documents with touch gestures ("move", "pinch", "zoom", "drag", "click"), 4) to annotate temporarily, permanently (Fig. 3), 5) to sketch.

The software versions were "Shariiing Research" (Fig. 3) and "Shariiing Advanced" 8 (Fig. 4). The principle of use is the same for these versions, the Advanced version's interface is more minimalist and offers more fluid interactions, and 3D models visualization is offered with the screen sharing.

For now users may only save an annotation on a project document as a new 2D image (screenshot). With Shariiing Research, the 3D model (.ifc, .obj) visualization and fluid interactions are possible, but it does not allow access to the model hierarchy. However, DCT offers visualization and touch 8 Shariiing specifications and functionalities https://www.shariiing.com/data/documentation/Shariiing%20specifications.pdf Template interactions with a distant user. Thus, when using Shariiing Advanced, it is possible to share a view from a BIM viewer or design software (e.g., Archicad, Cadwork, Nawisworks, etc.) directly to the collaboration environment, and to keep natural interactions and simple annotations (Fig. 4). Further, our research aims to better adapt the above mentioned functionalities to AEC needs.

In addition to some current software limitations, we must acknowledge the equipment limitations, such as the screen size and resolution, and team's collaboration methodology.

Digital Collaboration Sessions (DCS) description

The session's main purpose was project review, starting with a brief presentation by the students of their progress to the professors. An architect, a structure engineer and a construction specialist were representing the pedagogical participants of DCS. The choice of the present professionals depended on the session purpose and on the project progress stage. They provided professional expertise and also represented a project client.

For the Wood Challenge 2019, the mean session durations were augmenting with the project progress: 19 min in the beginning, 28 min in the end. In general minimum session duration was 13 minutes through all project progress, and maximum session time was also augmenting from 29 min for the first session to 53 min to the last one (Fig. 8). For Wood Challenge 2018, mean DCT duration was 23 min with max of 37 min and min of 18 min.

For Wood Challenge 2018 the design and construction subject was a pavilion 9 for a botanical garden in Nancy, France. From the 10 student teams, only 2 teams were using the DCT for their weekly meetings (Digital Collaboration Sessions) with the pedagogical team members during the Design phase. Both of these teams were using plans, sections, rendered images, quantifications and 3D models for design development and value engineering at the meetings (Fig. 5a). Only one team prepared a 4D model (Navisworks screenshot Fig. 5c, build structure Fig. 2a). However, during the construction, the students preferred to rely mostly on printed project documentation. The 4D model was consulted only once a day by one member of the team (construction management role) for a better understanding of the assembled details and for monitoring of the progress according to the schedule.

Together with the feedback (Sections 3.1, 3.2) on DCT improvements for AEC needs, students and professors suggested for the next year to introduce the DCT before the challenge. Thus, the table was used during autumn semester to work on a design project (reconstruction of an industrial site for student housing, residential buildings and a kindergarten) (Fig. 3). The teams had time to get experience with digital support for their weekly meetings, and to become independent users for their Wood challenge. However, not all of the sessions' participants had an equal amount of time to interact with the document due to a larger number of participants. Also, 4D simulations were introduced to the students, and some of them decided to integrate them into the final project folder (digital) along with the project plans, sections, 3D model, calculations and quantifications. Table1 synopsizes elements of DCS organization.

Finally, after training with the Design project, all the teams of Wood Challenge 2019 were using DCT for their weekly meetings with the pedagogical team during the Design phase of the challenge project (Fig. 6). A new version of collaboration software (Shariiing Advanced) was installed on the DCT, to answer students requests for more familiar to them 3D models view (from their personal 3D 9 Pavilions "Lignea camera"http://www.defisbois.fr/editions/edition-2018-lignea-camera/ a b c

Template modeling software interfaces) (Fig. 6a,b), and requests for more fluid interactions. All the teams were using a 3D model as a main discussion support. During the 2 final sessions, 5 student teams used 4D simulations (Fig. 6d) to illustrate a construction sequence and logics for the elements of the project.

Research questions

Naturally, every construction project is unique. A stakeholders team collaboration strongly depends on a project type. Their synchronous collaboration and decision-making depend meeting types, which require specific to the meeting objective documents and access to group interactions. In order to design a collaboration support tool with a well-adapted to AEC users interface and collaboration method. For this paper, we aimed to evaluate a presided usability and learnability of the digital collaboration Template support and to emphasize advantages and current limits of such tool through the users feedback. In addition, the experiment aimed to highlight user's needs for a better interactions with digital project documents, listed by document types. The feedback on perceived role of 3D and 4D models at construction planning discussions on the pre-construction phase. Also, for this paper, with DCS observations, we aimed to better portray decision-making dynamics and main aspects, such as: time of the session, documents used for discussion, interaction gestures and decision-making point. The DCT influence on pedagogy is in the scope of the interest as well. In addition to this paper, the research aimed to measure group collaboration and technology acceptance.

Feedback collection tools

The session's interactions were documented with video cameras and the table screen records. Also, participants' feedback was collected through a custom-built questionnaire and semi-guided interviews. Figure 7 resumes main feedback collection sources.

The first part of the questionnaire offered to session participants is to fill up the System Usability Scale (SUS) [START_REF] Brooke | SUS -A quick and dirty usability scale[END_REF] which is composed of ten traditional items to note on a Likert Scale. The scale is a free and quick tool to measure the system usability, however it provides quite reliable results to measure usability and learnability [START_REF] Sauro | When designing usability questionnaires, does it hurt to be positive?[END_REF] [START_REF] Brooke | SUS: A Retrospective[END_REF].

Accompanying the SUS scale, earlier, for feedback collection from similar digital collaboration experiments with professionals, the 4D Collab team also included open answer questions on usability. The question allowed to collect more complex feedback from the AEC professionals following the SUS first part of the questionnaire. To stay in correlation with the previous experiment records, the same questions follow the SUS part of the questionnaire for our pedagogical experiment feedback. Additional questions on 3D, 4D and planning complete this second part. The semi-guided interviews about DCT usability and requirements, specific to the AEC, complete this part of the feedback.

Also, the questionnaire for the student teams contained parts on group reflexivity [START_REF] Carter | Reflexivity, Effectiveness, and Mental Health in BBC-TV Production Teams[END_REF], a Technology Acceptance Model 3 (TAM 3) [START_REF] Venkatesh | Technology Acceptance Model 3 and a Research Agenda on Interventions[END_REF]) and a 4D BIM uses evaluation, however their results are not covered by this paper.

Findings summary

SUS score and usability feedback

In total we have collected a SUS from 9 users at Phase1 in 2018, and from 29 users in 2019 at Phase 2. With two main categories of population: students and professors; and one subcategory for the students by the studies background: architects, wood and civil engineers.

The feedback for the Wood Challenge 2018 emphasized the SUS score for all users (students and professors) as a mean score of 75 points (on a scale from 0 to 100, passing range starting from 68). Thus, according to a Rating Score summarized by Bangor et al. [START_REF] Bangor | Determining What Individual SUS Scores Mean: Adding an Adjective Rating Scale[END_REF], this result would be: rated as "good" in adjective ratings; filling into "acceptable" acceptability ranges; corresponds to a letter note "C". Also, in 2018, the professors mean score of 75.83 is slightly higher than the score from the students, at 74.58, but it stays relatively close to the students and All participants (see Table 2). Regarding the study domains (subcategory), the architecture students gave a much higher score than wood structures engineers. To summarize, these scores may be interpreted that in general, 2018 users are rather pleased with Digital Collaboration table, and find it usable and highly intuitive.

As of 2019 the mean SUS score for all users is 61.12. According to the Rating Score, this number is rated as "D", and being between "OK" and "Good" in adjective ratings. It is much lower than in 2018, an has a significant deviation. The professor result was a little higher than a year before, at 79,5, and it was very different from the student score of 56.87. The professors already had some experience with

Video observations

Semi-guided interviews

System Usability Scale (SUS)

Open answer questions (OAQ)

Team reflexivity TAM3, 4D BIM uses

Questionnaire

Template the Digital Collaboration table a year before and, even with updates, they still felt confident in the given score. However, in 2019 more student teams have participated at DCS than the year before, and not only those most open to innovation and digital collaboration, which has influence on technology acceptance in general. The students also had twice as many sessions with the DCT than their predecessors, and thus had a long-term and multiple uses perspective. As before, the architecture students gave a higher score than the engineers. The SUS scores are summarized in Table 2. Besides the abovementioned scores by users categories, there are additional scores. Most of the participants (79% with score 69,33) have confirmed that, in general, with the DCT they could perform their actions well (with no obstacles) during collaboration sessions. As for the participants who did not say that they could execute their intentions well (score 42.5, max 47.5), they would give most often mention that session discussion is very animated and they did not have enough time (or quick enough reflexes) to quickly visualize the documents they wished to use as the discussion support. Some of them mention that they prefer to use a pen and paper for decision-making.

Besides, the active users of CAD give slightly higher SUS scores than others, but the experienced 3D model users tend to give higher scores (76) than less experienced users (55). The participants with more field experience also tend to give a higher score (76) than others with less than 2 years of experience (59,8).Despite some low SUS scores from users, the added open questions (Section 3.2) portray a positive experience, and show again a good usability of DCT.

Despite the low number of participants, we analyzed the data statistically. First, in any group larger than 8 we verified whether the score distribution was normal with two tests: Shapiro-Wilk (SW) and D'Agostino's K 2 (DAK 2 ). None of the scores given by architects, engineers, professors, nor all respondents together violate the normality assumption (in SW p-value ranging from 0.196 to 0.647, W from 0.94 to 0.96; in DAK 2 p-value ranging from 0.268 to 0.521, K 2 from 1.30 to 2.64). However, since normality tests are of little power on small sample sizes, for investigating the similarities and differences between the groups we did not restrict ourselves to parametric tests (T-test; whether the variance was the same or not, decided by an F-test for equal variances -always different in our case), but also carried out two non-parametric ones (Kolmogorov-Smirnov (KS) and Mann-Whitney (MW)) (Fig. 8).

Fig. 8: the schematic representation of similar and different respondent groups by T-test, KS and MW tests: A -architects, E -engineers, C -civil engineers, P -professors. A continuous line: the scores are consistent with the hypothesis that the two groups come from the same distribution, according to all three of the tests. A disagreement between some of the tests makes it a dotted line. The absence of a line signifies

that all tests reject the null hypothesis and conclude that the populations are significantly different.

The professors group, P, the highest scores, stand out from the others: their scores are statistically significantly different from those of C and E, who gave the lowest scores (p-value < 0.01 in all tests). The group that resembles P the most is the architects (A), who came out to be similar to them in the first edition of the study (p=0.580 in T-test, 0.961 in KS and 0.500 in MW test; the statistics t=0.60, F=0.33, U=5.50 respectively) and different in the second one (p-value < 0.05 in all tests, t=-3.92, F=0.80, U=1.50), bringing about mixed results when taken together (different according to T-test and MW, p<0.01, and not dissimilar according to KS, p=0.072,). The pairs A and E and C and E are consistent with the assumption that the respondents' scores come from a same population. Groups A Template and C are close to conforming to the similarity hypothesis but not unanimously (similar according to MW, p<0.05, U=19.00, and different according to T-test and KS, p=0.079 and 0.059, t=1.93, F=0.60).

Summary of feedback and interviews

In general, session participants (users) find the DCT very ergonomic for meetings, it unites the documents well in a single environment and allows shared views of the same document for everyone around the table. Thus, it allows better understanding, fosters collaboration, and exchanges at the meeting around the table. Also users mention a "playful aspect" added by DCT, which creates a more informal setting for the meeting.

Regarding the document transfer at the table, users were glad to use quick wireless file drop from their laptops to the table to bring the last-minute modifications version of the document to the discussion. Some users said that digital support for the documents requires a better meeting preparation, and curiously, saw this aspect not as a disadvantage, but as an advantage which would help them to be more efficient in preparation to a meeting. However, in the beginning of the at the beginning of meetings, when all the documents were just starting to appear on the screen, it was hard for a presentation speaker to keep everyone's attention on the same document. Thus, to keep the focus of the users, the collaboration environment should better contain the most relevant documents to the discussion.

Visualization quality is the first of the more often mentioned benefits of the DCT, especially for 3D. Many users found a large screen to be well suited for visualization of detailed large documents (plans, sections, details, etc.), especially during review in a full-screen mode. They highlight a collective aspect of the visualization and possibility to zoom-in to view details quickly.

According to the observations, the visualization of PDF files was qualified as fluid, which was very important to review project documents. But the most emphasis was given by users to the benefits for 3D models visualization on a large screen with shared views. Indeed, according to observations a 3D model was always in the center of the discussion. In addition, users were glad to be able to share their laptop screen with a 3D or 4D model opened in their modeller (Archicad, SketchUp, Cadworks, Rhino, Navisworks) directly, without needing to export to other file formats.

Accessibility of interactions with documents is the second most often mentioned benefit of the DCT. Users have noticed progress on fluidity of actions with the latest version of the software. Users appreciate being able to zoom-in on a detail and then highlight problems with temporary or permanent annotations to explain them to others, or even to annotate simultaneously with their colleagues. A manageable 3D model navigation is also mentioned by users as one of the beneficial and essential interactions.

Many suggestions on DCT improvements were about annotation and drawing functions. More than a third of the experiment participants described the current drawing precision (line thickness, touch precision) as somewhat lackluster. Therefore, they preferred to make a double of the DCT sketch on a paper for better precision. Some suggested providing users with styluses.

Since 3D models were at the heart of most of the exchanges, many user suggestions and critiques were received about 3D visualization and navigation. For example, a few users stated that it is harder for them to understand or interact with 3D models and they prefer 2D documents. They suggest replacing 3D navigation with necessary pre-set point of view screenshots, to avoid the need to navigate through the views/model. When students were sharing their screens with 3D models (in the professional software) into the Shariiing, some have noticed delays between manipulation actions (move, zoom, rotate) and model response time. Thus a more efficient way to share screens is to be developed and a better preparation protocol of 3D model for the session, which must be run on a performant laptop, is to be identified.

The users also highlighted a difficulty of finding the right documents and also a need to stay connected to their project cloud services, to be able to have an easy access to all the documentation directly, without downloading them into the session.

The session results and feedback formalization tool and "tasks to do" before the next meeting tool were also requested to organize better the decision-making, and document decisions in a more detailed way than 2D annotated documents.

Template

Most of the users state that 3D visualizations are useful for decision-making on design development or value engineering. They have also agreed that 4D improves understanding of planning problems and is a useful asset for a collective decision-making on scheduling or construction strategies.

Digital Collaboration Session activities

We distinguish three main levels of interactions with DCT: visualization, manipulations, and annotations. Users may visualize 2D documents, 3D or 4D models. They may manipulate the Shariiing windows with: move, pinch, and rotate. Inside the sharing windows while visualizing the documents, "zoom" manipulation is also possible, along with annotations (drawings): temporary (disappearing), and permanent. Also, DCS participants had access to sketching on the Shariiing background table (Fig. 6f) and notebooks and pens. Naturally, users accompany their session with discussion (verbal communication), pointing, and mimicking gestures.

The major use of the DCT was visualization (Fig. 6c,d), accompanied by user discussion and pointing gestures (Fig. 5a,6b). Model manipulations were mostly used for project presentation and to fix a point of view to annotate a solution. Sketching and annotations (Fig. 6a,e,f) were used to support a solution proposition and to suggest modifications, however not every session benefited from the annotation function. Since the duration of manipulations and annotations are lower than visualization, we will count these "actions" throughout the activity (Fig. 9).

The DCS duration depended mostly on a project design and technical solutions quality. For instance, teams presenting only 2D documents, or only 3D models, or 3D and 4D models did not show a shorter time depending on the represented document types. As a main support for decision making and discussions, participants felt more inclined to use a 3D model. They also tended to solve all the questions with only one document as a decision making support (2D or 3D) (see Fig. 10 for sources of the shared views on the models from students' laptops to Shariiing Advanced). Most of the time, a relevant decision would be made in the middle of a session, and would then be followed by additional suggestions on design or engineering. 4D models were used only in the beginning of the meeting to visualize construction sequence logics, but yet further discussion was supported by a 3D model due to better interactions.

Conclusions

This paper summarizes the pedagogical experiment on synchronous collaboration at project review meetings with digital support (Digital Collaboration Table -DCT). The experiment context of the pedagogical exercise Wood Challenge was an opportunity to follow the collaboration of student teams and professors from the design to construction, and to assist at weekly project review meetings with DCT.

Such context allowed us to evaluate DCT usability and learnability from active and frequent user perspectives in the case of a real construction project (small wooden structure). Also, the study highlighted user interactions with digital project documents during their collaboration sessions, in Template particular 3D and 4D model interactions. The analyzed user activities at collaboration sessions showed that 3D models are principally in the middle of the discussion, and thus must have the most fluid interactions. The DCT must provide not only the 2D annotations but also to be able to leave BIM model annotations.

The Digital Collaboration Table represents a useful support for the project document's visualization, and for the document's manipulations and annotations. Also, it is a valuable support to more democratic collaboration of the project documents and to decision-making. However, user feedback suggests several categories for further improvements of the support and its adaptation to AEC project review. Among the key suggestions are: the need for a simple touch interface adapted to particular use cases for easier manipulation and annotation in 3D and 4D models; the need for automatic documentation of collaboration results and their integration into the BIM model structure; the need for an augmented sketching function for improved precision; the need for further integration of the table into a collaboration system connected to the cloud. These further improvements will be integrated into a prototype for a new collaborative 4D-based decision-making device by the 4D Collab research project team.

Figure 1 :

 1 Figure 1: Schema of the digital collaboration experiment steps

Figure 2 :

 2 Figure 2: Examples of Wood Challenge projects

Figure 3 :

 3 Figure 3: Digital Collaboration Session with Shariiing Research: a,b annotation of façade detail, c. 3D section visualization and discussion

Figure 4 :

 4 Figure 4: Digital Collaboration Session with Shariiing Advanced, interactions with 3D models

  Figure 5. a. Collective decision-making at Design phase in 2018 b.3D model review at Construction phase c.4D simulation for one module assembling length estimation and progress monitoring

Figure 7 :

 7 Figure 7: Summary of the feedback collection steps for the pedagogical experiment

Figure 10 :

 10 Figure 10: Information sources for DCS No 1-4 for Wood Challenge 2019 (shared views from laptops for 3D and 4D)

Table 1 :

 1 Digital Collaboration summary for Wood Challenge 2108 and 2109, for Design Project

	Wood Challenge 2018	Design Project	Wood Challenge 2019

Table 2

 2 Summary of SUS scores for digital collaboration table by project roles

			All participants	Students	Professors	Architects	Wood Engineers	Civil Engineers
	2018	Mean Score	75	74,58	75,83	78,13	67,5	-
		Deviation	6,96	8,12	5,2	4,73	10,60	-
		Count	9	6	3	4	2	-
	2019	Mean Score	61,12	56,88	79,5	59,17	56,67	53,75
		Deviation	15,71	13,77	10,37	11,18	18,16	11,15
		Count	29	24	5	9	9	6

https://www.shariiing.com/

https://www.immersion.fr/

https://www.4dcollab-project.eu/

Original French Défis du Bois (http://www.defisbois.fr/)

École Nationale Supérieure des Technologies et Industries du Bois (http://www.enstib.univ-lorraine.fr/fr/)

Orig. Fr. «Architecture Bois Construction"( http://www.nancy.archi.fr/fr/master-genie-civil-1.html)

Orig. Fr. Défis du Bois (http://www.defisbois.fr/)

Acknowledgements

This study was developed under the patronage of "Agence Nationale de la Recherche" No.ANR-16-CE10-0006-02 (FR) and "Fonds National de la Recherche" (LU), as a part of the 4D Collab research project. Authors acknowledge Wood Challenge teams for participation and "Immersion" for technical support.


Antoine Blaise Kama

Romain Génois

Florian Massuyeau

Mamadou Sidibé

Cheikh A K Diop

Romain Gautier

Antoine Blaise Kama

Cyclohexylammonium sulfanilate: A simple representative of the chiral materials containing only achiral building units

come

Introduction

The synthesis of noncentrosymmetric (NCS) compounds is of high importance in optics or chemistry owing to their interesting physical properties such as catalysis, dichroism, piezoelectricity, ferroelectricity, pyroelectricity, or Second Harmonic Generation (SHG) [1][2][3][4][5][6][7][8][9][10]. These multiple applications require simple synthetic methods of NCS compounds. A well-known method to produce successfully such solids is to use enantiomerically pure molecules because such units must pack into chiral crystal structures [11]. But this method is commonly expensive as the molecules must be enantioenriched and should survive the growth methods without racemization [12]. Another approach is to use achiral building blocks [1,[13][14][15]. However, in this method, the arrangement of the achiral building blocks in the solid must be NCS. For this reason, understanding the packing of achiral molecules into NCS arrangements is a key for the future design of noncentrosymmetric (NCS) functional materials. Previous works reported SHG active chiral compounds from NCS, achiral building units [16,17]. Herein, we aim at understanding the packing of two achiral molecules through hydrogen bonding into an SHG active chiral compound.

The NCS achiral sulfanilate anion was previously stabilized into diverse materials with counterions such as ammonium, rubidium, lithium or potassium [18][19][20][21]. In this letter, we used the NCS achiral cyclohexylamine and obtained a new chiral compound exhibiting a Second Harmonic Generation (SHG) response. A statistical analysis of the arrangement of the sulfanilate anion with different CS or NCS cations provides new insights in the future design of NCS materials.

Materials and methods

Sulfanilic acid (99%) and cyclohexylamine (99%) were purchased from Aldrich and used without further purification. Cyclohexylammonium sulfanilate was prepared by mixing cyclohexylamine (0.04 mol) and sulfanilic acid (0.04 mol) in distilled water at room temperature. The solution was stirred for two hours. Large colourless crystals suitable for X-ray diffraction were obtained after slow evaporation of the water. For spectroscopic measurements, these colourless crystals were firstly ground with KBr and pressed into pellets. FT-IR spectra were obtained with a Bruker Vertex 70 instrument, 100 scans were collected with ⇑ Corresponding authors. E-mail addresses: antoineblaise.kama@ucad.edu.sn (A.B. Kama), Romain. Gautier@cnrs-imn.fr (R. Gautier). a resolution of 4 cm À1 from 400 to 4000 cm À1 . A background spectrum was subtracted. Diffuse reflectance spectrum of the ground crystals was collected with a Perkin Elmer UV-visible-NIR spectrometer (Lambda 1050) equipped with an integrating sphere. The obtained data were treated by Kubelka-Munk transformation. Single-crystal X-ray diffraction was performed using a Bruker-Nonius Kappa CCD diffractometer (MoKa radiation/crystal to detector distance = 60 mm). Absorption corrections were considered using SADABS [22]. Direct methods were used to determine the crystal structure through the program SIR2004 [23]. The crystal structure was refined with SHELXL-2013 [START_REF] Sheldrick | SHELXL-2013[END_REF]. Additional symmetry elements were checked using PLATON [START_REF] Spek | [END_REF]. More information on the crystal structure is available in Table S1-3. Differential Scanning Calorimetry (DSC) measurements was carried out with a Setaram Sensys Evo under Argon flow, from room temperature to 800 °C, with a heating rate of 5 °C.min À1 . A Ti:Sa laser from Spectra Physics (Hurricane model) delivering pulse of 100 fs at 800 nm (1 kHz) was used to detect SHG signals. SHG was collected at 400 nm with a streak camera C7700 from Hamamatsu coupled with a spectrometer from Princeton instruments.

Results and discussion

Structure description

The compound crystallizes in orthorhombic system (space group P2 1 2 1 2 1 ). The asymmetric unit contains the cyclohexylammonium cation and the sulfanilate anion. The crystal packing shows supramolecular self-assembly through the three axes a, b and c, resulting from the interactions sulfanilate-sulfanilate and sulfanilate-cyclohexylammonium.

The sulfanilate-sulfanilate interactions through N-HÁÁÁO-S connections generate chains. The cyclohexylammonium connects these chains via hydrogen bonding N-HÁÁÁO-S, leading to a 3D network of hydrogen bonds (Fig. 1). Comparing with previously reported sulfanilate compounds with counterions such as ammonium, rubidium, lithium or potassium [18][19][20][21], this resulting crystal structure is chiral. The main difference between the different crystal structures is the symmetry of the cations: while cations are centrosymmetric in these previously reported compounds, cyclohexylammonium is non-chiral but polar (Fig. 2). Thus, the use of this polar unit might be an important parameter for inducing a NCS material. In our compound, the polar units pack along perpendicular 2 1 axes. For this reason, the net dipole moments of the molecules are cancelled out but chirality is generated from the molecular packing. However, the analysis of crystal habit did not allow to simply distinguish between the opposite chirality senses. To better understand the role of the symmetries of the cations/anions on the final packing, one can performed statistical analysis of the Cambridge Crystallographic Database. Over 88 crystal structures containing the sulfanilate anion, 24 which contain molecular cations were selected for further investigation. Our analysis shows that the ratio of NCS crystal structures is 29% (close to the ratio for all compounds: 22%). Among the CS structures, 41% result from the combination of sulfanilate with NCS cations. On the other hand, among the NCS structures, 86% result from the combination of sulfanilate with NCS cations. The statistical results also show that the packing of sulfanilate with NCS cations through hydrogen bonding network is more likely to lead to NCS structures (54%) than when using CS cations (46%) as if the overall occurence of NCS structures is much lower (29%). For this reason, one can conclude that combining two NCS molecules might be an interesting strategy to target NCS compound. This could be explained by the fact that each NCS molecule offers an acentric environment for the packing of the other.

UV/Visible and FT-IR spectra

Diffuse reflectance shows strong absorption below 350 nm for the title compound. This intense UV absorption is mainly due to p-p * transition in the aromatic nucleus, confirming the presence of phenyl (sulfanilate) (Fig. 3). The low absorption around 375 nm can be identified as the substitution effect on the phenyl, namely NH 2 and SO 3 groups. The FT-IR Spectrum is shown in Fig. 4. The full attribution of the main absorption bands is available in Supporting information (Table S4). Absorption bands in the range of 3450-3200 cm À1 are assigned to t N-H vibration modes.

d N-H vibration mode is also located from 1650 to 1600 cm À1 and c N-H is in the range of 850-820 cm À1 . From 3100 to 2850 cm À1 , there are several bands attributed to t C-H of the aromatic nucleus and the t C-H (CH 2 ) of cyclohexyl. The ones at 600 and 700 cm À1 are assigned to d C-H of the aromatic nucleus. d C-H (CH 2 ) of cyclohexyl also appears from 1466 to 1387 cm À1 . According to the literature [ [START_REF] Zhaoa | [END_REF]27], the vibration tape at 1214, 1184 and 1169 cm À1 are due to t as of -SO 3 À group while the ones at 1030 cm À1 and 1011 cm À1 are assigned to t s of the same group. t C-N appears at 1000 cm À1 .

Second Harmonic Generation measurements

The differential scanning calorimetry performed on the sulfanilate shows its decomposition at about 250 °C. Thus, Second Harmonic Generation measurement can be carried out without the risk of important degradation due to the excitation power laser (Fig. S1). Every noncentrosymmetric material except the ones in the point-group 432 can be SHG active [7,28]. As our compound crystallizes in the space group P2 1 2 1 2 1 , this material is potentially SHG active. To confirm the noncentrosymmetry of this material, SHG measurement was performed with potassium dihydrogenphosphate (KDP) as reference (Fig. 5). The measurements performed on powder samples at k = 800 nm show the same response at 400 nm confirming the simple synthesis of noncentrosymmetric compound from the achiral building units.

Conclusion

The new compound cyclohexylammonium sulfanilate was synthesized at room temperature by mixing sulfanilic acid and cyclohexylamine in 1/1 M ratio. The material is chiral and crystalizes in P2 1 2 1 2 1 space group. The crystal structure consists of a tridimensional network of hydrogen bonds formed by chains of sulfanilate anions interconnected with cyclohexylammonium cations. A statistical analysis showed that the acentric polar sulfanilate is more likely to lead to NCS crystal structures when using NCS cations than CS ones. In this letter, the simple achiral building units (cyclohexylamine and sulfanilic acid) lead, through an easy synthetic approach, to a chiral material exhibiting a SHG response. Thus, we believe this investigation will serve as a simple illustration of the induction of chiral materials which do not require enantioenrichment.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Crystal structure of cyclohexylammonium sulfanilate (Hydrogen bonds are represented in green dotted lines). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 4 .

 4 Fig. 4. FT-IR spectrum of cyclohexylammonium sulfanilate compound.

Fig. 5 .

 5 Fig. 5. Second Harmonic Generation response of cyclohexylammonium sulfanilate with incident beam at k = 800 nm (Inset: SHG response of the standard KDP).

Fig. 3 .

 3 Fig. 3. Kubelka-Munk transformed reflection spectrum of cyclohexylammonium sulfanilate.

Acknowledgement

We would like to thank Stéphane Grolleau for performing the thermal analyses. ABK thanks the Campus France Agency for international mobility. This work was supported by Centre National de la Recherche Scientifique (PICS, project "RacOpAc").

Declaration of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https://doi.org/10.1016/j.matlet.2019.01.034.


Alaa Khreis

Philippe Ciblat
email: ciblat@telecom-paristech.fr

Francesca Bassi

Pierre Duhamel
email: duhamel@l2s.centralesupelec.fr

Multi-Packet HARQ with Delayed Feedback

In current wireless communication systems, the feedback required by the Hybrid Automatic ReQuest (HARQ) mechanism is received with some delay at the transmitter side. To alleviate this issue, parallel Stop-and-Wait HARQ is usually employed. In this paper, we propose a multi-packet HARQ protocol (also called superposition coding or multi-layer HARQ) to improve the user's delay distribution and increase the throughput, without any additional feedback such as Channel State Information. The performance analysis, provided from an informationtheoretic point-of-view, shows that the proposed protocol offers better delay distribution, higher throughput and lower message error rate compared to the conventional parallel Stop-and-Wait HARQ, at the expense of increased decoding complexity.

I. INTRODUCTION

Hybrid Automatic Repeat ReQuest (HARQ) with Incremental Redundancy (IR) is used in wireless communication systems to improve communication reliability [START_REF] Sesia | LTE: the Long Term Evolution -from Theory to practice[END_REF]. In HARQ, the receiver feeds back an Acknowledgment (ACK) (resp. an Negative ACK) to the transmitter if the receiver succeeds (resp. fails) to decode the current message. If ACK is fed back, the transmitter sends a packet related to a new message during the next timeslot. If NACK is fed back and the maximum retransmission credit is not exhausted, the transmitter sends a redundant packet associated to the current message.

Due to propagation time and reverse link scheduling, the feedback associated to a sent packet is available to the transmitter with a delay of multiple time-slots. The communication system is idle in-between if Stop-and-Wait HARQ protocol is used [START_REF] Lin | Error Control Coding[END_REF]. A conventional approach to compensate for this issue is to initiate, during the unused time-slots, Stop-and-Wait HARQ processes corresponding to other messages. This scheme, called parallel Stop-and-Wait HARQ [START_REF] Lin | Error Control Coding[END_REF], allows the transmission of multiple messages in parallel, each of them employing an independent Stop-and-Wait HARQ process. Parallel Stop-and-Wait HARQ improves the throughput but does not mitigate the delay of the received messages, which is related to the maximum retransmission credit and to the feedback delay. The protocol proposed in this paper enables the transmitter to anticipate the feedback This work was supported by the Labex Digicosme PhD scholarship from Université Paris-Saclay under the grant called "Coccinelle" by sending, in advance to its reception, data related to unacknowledged messages. This is accomplished using superposition of packets, also called multi-packet or multi-layer transmission in the literature [START_REF] Hamss | Increasing the throughput of HARQ via multi-packet transmission[END_REF]- [START_REF] Steiner | Multi-layer broadcasting hybrid-ARQ strategies for block fading channels[END_REF].

To the best of our knowledge, none of the previous works on superposition coding in the context of HARQ considered the possibility of delayed feedback. Therefore the proposed protocol, described in Section III, is significantly novel since it allows to counteract the delayed feedback as well as to improve the throughput. In [START_REF] Hamss | Increasing the throughput of HARQ via multi-packet transmission[END_REF], [START_REF] Jabi | Multipacket Hybrid ARQ: Closing Gap to the Ergodic Capacity[END_REF], superposition coding without feedback delay is employed, and outdated Channel State Information (CSI) is available at the transmitter side to optimize the choice of superposed packets. The protocol in [START_REF] Zhang | Superposition-Coding-Aided Multiplexed Hybrid ARQ Scheme for Improved End-to-End Transmission Efficiency[END_REF] considers feedback on the Transport Control Protocol (TCP) layer, where each TCP frame corresponds to a pre-defined number of retransmissions with superposed packets. In [START_REF] Takahashi | HARQ for Predetermined-Rate Multicast Channel[END_REF], the authors propose a simple superposition modulation based on QPSK (Quadrature Phaseshift Keying), with a single possible retransmission and without feedback delay. In [START_REF] Assimi | Packet combining for multi-layer hybrid-ARQ over frequency-selective fading channels[END_REF], the authors focus on practical joint detection of superposed packets in multilayer HARQ without feedback delay. In [START_REF] Steiner | Multi-layer broadcasting hybrid-ARQ strategies for block fading channels[END_REF], the authors show that multi-layer HARQ (considered there with no feedback delay) significantly increases the throughput.

An alternative method to improve the conventional parallel HARQ is to use time sharing and rate adaption policies, as in [START_REF] Trillingsgaard | Generalized HARQ Protocols with Delayed Channel State Information and Average Latency Constraints[END_REF] and [START_REF] Szczecinski | Rate Allocation and Adaptation for Incremental Redundancy Truncated HARQ[END_REF]. This requires, however, knowledge of the CSI at the transmitter side. Moreover, time-sharing does not exploit the potential of Multiple Access Channel (MAC) communication, while superposition does.

The main contribution of this work is a protocol that superposes an additional layer of redundant packets to the parallel Stop-and-Wait HARQ protocol. In the superposed layer, the transmitter may perform retransmissions of a message even before having received any feedback about it. The selection of the superposed packets is based solely on the delayed ACK/NACK feedback (no additional CSI). The proposed protocol improves the performance of parallel Stop-and-Wait HARQ in terms of delay distribution, throughput and message error rate at the expense of decoding complexity, since the receiver must decode superposed packets. This paper is organized as follows: Section II defines the system model. We explain the proposed HARQ protocol in Section III and the corresponding receiver is analyzed from an information theoretic point of view in Section IV. Performance metrics in comparison to conventional HARQ are presented in Section V. Concluding remarks are drawn in Section VI.

II. SYSTEM MODEL

We consider slotted point-to-point transmission where each time-slot corresponds to N channel uses. During each time-slot t, the transmitter sends N symbols stacked in vector x t . This vector may be composed of a packet or a superposition of packets, as it will be explained in Section III. The received signal at time-slot t is

y t = h t x t + n t , (1)
where n t is an additive white Gaussian noise vector, with zero-mean and variance per component equal to N 0 . We consider a Rayleigh flat fading channel with coherence time equal to the time-slot duration. The channel is fixed during a time-slot, but has independent realizations at each time-slot. We also assume perfect CSI at the receiver. The channel gain is denoted by g t where

g t = |ht| 2
N0 . The transmitter has a set of messages {m k } k∈N+ to send. Each message contains N R bits of information, where R is the rate. A message m k is encoded via a mother code of rate R 0 ∈ R + and then punctured into C modulated packets of length N . Consequently, we have R = R 0 C. The -th packet related to message m k is denoted by p k ( ) with ∈ {1, • • • , C}. The feedback is error-free and only composed of ACK or NACK of the considered messages. We assume a feedback delay of T time-slots, which means that the feedback related to a transmission performed in time-slot t is received by the transmitter just before the beginning of time-slot t + T . The case T = 1 corresponds then to a no-delay feedback. We assume moreover that this delay is due to the return channel and not to the decoding time at the receiver, which means that the receiver knows at the end of time-slot t if the messages related to the packets transmitted at time-slot t are successfully decoded or not. A message is said in timeout if it is not ACKed by CT time-slots after its first transmission, corresponding to the timeout in conventional parallel HARQ.

III. PROPOSED PROTOCOL

In the proposed protocol, at each time-slot the transmitter selects a packet p k ( ), based on the ACK/NACK feedbacks, as in conventional parallel Stop-and-Wait HARQ. The transmitter may superpose to p k ( ) a second packet p k ( ), with k = k, even if there is not any feedback on previous transmissions of message m k yet. The idea is to send a redundant packet without waiting for the feedback to arrive at the transmitter side, which enables the receiver to possibly decode m k without waiting for the next Stop-and-Wait HARQ round.

In order to keep the same energy at each time-slot, the superposed packet, belonging to the second layer, uses 100(1 -α)% of the predefined energy per timeslot, while the packet sent by the first layer uses 100α% of the energy, with α ∈ [0, 1]. The influence of α will be investigated in Section V. The transmit vector x t is given by:

p k ( ), if no superposition, √ αp k ( ) + √ 1 -αp k ( ), if superposition.
We note that the case of α = 1 corresponds to the conventional parallel Stop-and-Wait HARQ.

At the beginning of time-slot t the transmitter knows the ACK/NACK related to the messages sent up to timeslot t -T (because of the feedback delay). According to this knowledge, the transmitter selects the packets to include in x t . As anticipated, the choice of the packet in the first layer corresponds to conventional parallel HARQ. Therefore, if packet p k ( ) was sent at time-slot t -T , the reception of a NACK relative to message m k just before time-slot t triggers the transmission of another redundancy packet p k ( + 1), as long as < C. Otherwise, the reception of an ACK of m k triggers the transmission of a packet p k (1) associated with a new message m k (never transmitted before). The selection of the superposed packet in the second layer is done according to the following principles: i) superposing packets related to the most recent messages of the first layer to reduce the delay, ii) superposing unsent redundant packets to reduce the message error by using transmit diversity. Based on these principles, we describe the selection strategy by the following rules (ordered by priority), which determine the choice of the superposed packet in the second layer: 1) A packet p k ( ) cannot be superposed if message m k is in timeout or previously ACKed. 2) As long as there are unacknowledged messages with unsent packets, the superposed packet is the unsent packet of the lowest index of the most recent message m k , with k = k (different messages in the two layers).

3) If the transmitter already sent all the packets of all the unacknowledged messages that are not in timeout, the superposed packet is the packet with the lowest index that was not previously sent in the second layer. (Notice that this packet has been already sent once, in the first layer). 4) No packet is superposed to a packet of the first layer that has = C. The first rule prevents larger delays than those provided by conventional parallel HARQ, while the fourth rule reduces the probability to drop messages by forbidding interference during the last retransmission. According time-slot

1 2 3 4 5 6 7 8 9 layer 1 p 1 (1) p 2 (1) p 3 (1) p 1 (2) p 2 (2) p 4 (1) p 1 (3) p 5 (1) p 4 (2) layer 2 p 1 (2) p 2 (2) p 3 (2) p 3 (3) p 1 (3) p 4 (2) p 5 (2) F t {1} N {1, 2} N {2, 3} A , {1} N {1} N {1} N {1, 4} N {1, 4} N {4, 5} N {4, 5} N TABLE I: A realization of the proposed protocol.
to this protocol, one can check that, at each time-slot, at most T messages are not previously ACKed nor in timeout, which means that the feedback at each timeslot contains at most T ACK/NACKs. In Table I, we provide one example of our protocol, with C = 3 and T = 3. We denote by {•} A (resp. {•} N ) the set of message indexes triggering ACK (resp. NACK) feedback. The notation F t stands for the output of the receiver at time-slot t. We remind that we consider instantaneous decoding at the end of the time-slot t, but F t will be available at the transmitter side as a delayed feedback after T time-slots.

IV. RECEIVER ANALYSIS

At the end of time-slot t, the receiver considers the observations of the most recent CT time-slots, corresponding to the maximum delay of the conventional parallel Stop-and-Wait HARQ. Since there are T parallel HARQ processes, there are at most T undecoded messages in this observation window. Therefore, the receiver attempts to decode these messages.

The output of the receiver is the feedback vector F t , which will be available at the transmitter at the beginning of time-slot t + T . The feedback vector F t contains the ACK/NACK bits corresponding to the messages that i) are object of decoding at time-slot t, and ii) will not be in timeout at time-slot t+T . We notice that attempting to decode all the messages, including the ones that will be in timeout, is beneficial because it helps in removing the interference introduced by the superposition. This can be seen in the example in Table I. In time-slot 8, the receiver attempts to decode m 1 , m 4 and m 5 . Since m 1 will be in timeout by time-slot 10, F 8 contains only information about m 4 and m 5 . At time-slot 11, when F 8 will be available at the transmitter, any feedback information about m 1 would be useless. However, attempting to decode m 1 is beneficial since it allows to remove the interference with message m 4 on time-slot 6.

In the next Subsection we give an information theoretic characterization of the performance of the receiver.

Information theoretic characterization of the receiver

Let M be the set of messages that the receiver is attempting to decode at time-slot t. If the receiver successfully decodes the subset D ⊆ M and none of the messages in M \ D, we say that the decoder operates in the rate region R D . The set D, along with the rules of the transmit protocol, allows to obtain F t . In order to characterize the decoding outcome, we i) evaluate the rate region R D for every possible D ⊆ M; and ii) determine, on the basis of the available observations, the operating rate region R D of the receiver. By definition, R D is given by the union of rate regions where the messages in D are successfully decoded (alone or jointly with other messages in M \ D), excluding the regions where the messages in D are jointly decoded with at least another message in M \ D. By construction of the system, the receiver can see the messages as users of a MAC channel. For a set of users S, R M AC(S) is the MAC rate region of users S considering the messages from users outside S as noise [START_REF] Bandemer | Simultaneous nonunique decoding is rate-optimal[END_REF]. We consider first the case D = ∅. The region where the messages in D, and possibly other messages in M, are successfully decoded is the union of the MAC rate regions of any set of users that includes D, i.e., D⊆S R M AC(S) [START_REF] Bandemer | Simultaneous nonunique decoding is rate-optimal[END_REF]. The region where the messages in D are successfully decoded, jointly with at least another message in M, is the union of the MAC regions of any set that includes D and at least another user from M \ D, i.e., D⊂S,S =D R M AC(S) [START_REF] Bandemer | Simultaneous nonunique decoding is rate-optimal[END_REF]. We deduce the rate region in (2):

R D =   D⊆S R M AC(S)       D⊂S , S =D R M AC(S )     = R M AC(D)   D⊂S,S =D R M AC(S)   . (2)
Since the regions R D , for all possible D ⊆ M form a partition by construction, the region R D=∅ is the complementary of the union of all rate regions for D = ∅, i.e.,

R ∅ = D⊆M,D =∅ R D = D⊆M,D =∅ R D . (3)
Then, to determine whether the receiver operates in R D , for any D ⊆ M, it is enough to verify whether the receiver operates within or outside the set of MAC regions involved in (2) and (3). The receiver operates in the MAC rate region R M AC(S) , for a set of messages S, if the following set of inequalities is satisfied [START_REF] Bandemer | Simultaneous nonunique decoding is rate-optimal[END_REF]:

j∈T R j ≤ I(X T ; Y |X S\T ), for all T ⊆ S, (4)
where Y represents the observations in the window of size CT time-slots, X T represents the sent packets relative to the messages in T , and X S\T is interpreted likewise. The packets relative to messages that are not in S but are in Y are treated as interference. We also have R j = R. The mutual information I(X T ; Y |X S\T ) can be calculated by reading the observations in the window of size CT , and cumulating the mutual information corresponding to the messages in T . In this process, we need to consider that: 1) some packets are superposed, and sent with different power fractions, 2) the same packet may be transmitted more than once, 3) messages which have been already decoded in the past may allow to eliminate interfering packets in the observations. In Table I, R D corresponding to D = {m 2 , m 3 } at timeslot t = 3 is obtained thanks to (2) as:

R D = R M AC({m2,m3}) R M AC({m1,m2,m3}) . (5)
The MAC rate region R M AC({m2,m3}) is given by:

     R ≤ log(1 + αg2 1+(1-α)g2 ) + log(1 + (1 -α)g 3 ); R ≤ log(1 + αg 3 ); 2R ≤ log(1 + αg2 1+(1-α)g2 ) + log(1 + g 3 ),
where packets corresponding to message m 1 are considered as interference. R M AC({m1,m2,m3}) is given by:

                         R ≤ log(1 + g 1 ) + log(1 + (1 -α)g 2 ); R ≤ log(1 + αg 2 ) + log(1 + (1 -α)g 3 ); R ≤ log(1 + αg 3 ); 2R ≤ log(1 + g 1 ) + log(1 + g 2 ) + log(1 + (1 -α)g 3 ); 2R ≤ log(1 + g 1 ) + log(1 + (1 -α)g 2 ) + log(1 + g 3 ); 2R ≤ log(1 + αg2 1+(1-α)g2 ) + log(1 + g 3 ); 3R ≤ log(1 + g 1 ) + log(1 + g 2 ) + log(1 + g 3 ).
This characterization provides the receiver's performance for capacity-achieving codes.

V. NUMERICAL RESULTS

We present here numerical results, via computer simulations, of the proposed protocol in comparison to conventional parallel Stop-and-Wait HARQ, both with C = 4, T = 3 and R = 0.8, for capacity-achieving codes. HARQ-IR is implemented as described in Section II. In Fig. 1a, we plot the throughput which is the average number of correctly received information bits per channel use. The proposed protocol offers significant throughput gain in comparison to conventional parallel HARQ for any Signal to Noise Ratio (SNR) at α = 0.6 and α = 0.8. E s is the energy consumed for sending one symbol. In case of superposition, we remind that the energy is shared between superposed symbols with the proportion α for the layer 1. The proposed protocol also achieves lower Message Error Rate (MER) than the conventional parallel HARQ, as it can be seen in Fig. 1b. The MER is defined as the average ratio of the number of dropped messages over the number of sent messages. The performance of the proposed protocol depends on the choice of the power fraction α. Therefore, we plot in Fig. 2 both throughput and MER, at E s /N 0 = 0dB, versus α. The power fraction α can be numerically optimized and fixed for each desired SNR depending on the application requirements. Further optimization of the power allocation is possible, but is out of the scope of this work. The average delay, which is the average number of elapsed time-slots until the receiver successfully decodes a message, is presented in Fig. 1c. In addition to lower average delay, the proposed protocol offers a better delay distribution. The delay distribution represents the proportion of successfully delivered messages for each value of delay. Fig. 3a shows that, due to parallel Stop-and-Wait HARQ protocol, retransmissions occur every T = 3 time-slots. Thus, a message can be decoded only with a delay of 1 (by decoding the first packet), 4 (by decoding the first retransmission), 7 (by decoding the second retransmission) or 10 time-slots (by decoding the last retransmission) for C = 4. However, due to superposition in the proposed protocol, the receiver can decode a message with a finer granularity of delays, and delays of 1, 2,. . . ,10 time-slots are possible, as it can be seen in Fig. 3b. We observe that the probability to have higher delay (such as 4 or more) is smaller with our proposed protocol.

VI. CONCLUSION

A multi-packet HARQ protocol when feedback is delayed has been proposed. Information-theoretic analysis of the receiver shows that the proposed protocol offers a smaller average delay, a better delay distribution, a higher throughput, and a lower message error rate than the conventional parallel Stop-and-Wait HARQ. The proposed protocol requires at the receiver side a joint decoding of the superposed packets. Future works might focus on implementing the protocol with practical channel encoders and decoders, creating other new protocols with respect to other rules depending on the application, or managing more relevantly the interference at the transmitter side since the messages are sent by the same transmitter.

  Proposed protocol, α = 1 Proposed protocol, α = 0.98 Proposed protocol, α = 0.8 Proposed protocol, α = 0.6 (a) Throughput of the proposed protocol.

  Proposed protocol, α = 1 Proposed protocol, α = 0.98 Proposed protocol, α = 0.8 Proposed protocol, α = 0.6 (b) MER of the proposed protocol.

  Average delay [time-slots] Es/N0 [dB] HARQ-IR Proposed protocol, α = 1 Proposed protocol, α = 0.98 Proposed protocol, α = 0.8 Proposed protocol, α = 0.6 (c) Average delay of the proposed protocol.

Fig. 1 :

 1 Fig. 1: Performance of the proposed protocol.

Fig. 2 :

 2 Fig. 2: Throughput and MER of the proposed protocol for different power fractions α at 0dB.


Alaa Khreis

Philippe Ciblat
email: ciblat@telecom-paristech.fr

Francesca Bassi

Pierre Duhamel
email: duhamel@l2s.centralesupelec.fr

Throughput-efficient Relay assisted Hybrid ARQ

Reliable data transmission within wireless communication systems can be obtained via various means, including (i) Hybrid Automatic Repeat reQuest (HARQ) mechanisms which allow retransmission of not-correctly decoded packets; (ii) Additional nodes, called relays, which may also help the transmission by retransmitting these packets. An efficient combination of both techniques is therefore of great interest. This paper proposes a new relay assisted HARQ protocol aiming at maximizing the system throughput. The main idea is to allow the source to transmit a new message during the same time slot as the relay is retransmitting some previous message. By using efficient interference canceler at the destination, the numerical results show significant throughput gain compared to standard approaches working separately on each message.

I. INTRODUCTION

We consider a wireless communication where a message is sent from one source to one destination. When the decoding fails at the destination side, it is now usual to re-encode the message into other packets retransmitted by the source (known as Hybrid Automatic ReQuest -HARQ- [START_REF] Lin | Automatic-repeat-request error control schemes[END_REF]). Another way to improve the communication is to add one relay along the route between the source and the destination. Assuming the destination does not decode correctly the message but the relay does, the relay retransmits some packet related to this message and mimics either a multi-hop routing or an ARQ retransmission mechanism. In this paper, the main objective is to combine these complementary approaches into new HARQ protocols taking into account the presence of relays.

As HARQ mechanisms (without the presence of relays), one can mention Chase Combining (CC) [START_REF] Chase | Code combining -a maximum likelihood decoding approach for combining an arbitrary number of noisy packets[END_REF] where the packet related to the message is retransmitted identically, all received packets corresponding to the same message being combined at the receiver. Another technique is Incremental Redundancy (IR) [START_REF] Mandelbaum | An adaptative-feedback coding scheme using incremental redundancy[END_REF] where the packet related to the message contains other redundancy bits which are decoded jointly with the previous ones. The performance of HARQ is usually evaluated via the following metrics: Throughput and Message Error Rate (MER) [START_REF] Lin | Automatic-repeat-request error control schemes[END_REF], [START_REF] Martret | Analytical Performance derivation of Hybrid ARQ Schemes at IP layer[END_REF]. In addition, HARQ protocol can be modeled as a Markov Chain whose transition probabilities enable us to evaluate the previously-mentioned metrics [START_REF] Badia | Markov analysis of selective repeat type II hybrid ARQ using block codes[END_REF], [START_REF] Chen | A novel Markov-chain-based method for throughput analysis in truncated cooperative HARQ systems[END_REF].

Many relaying protocols have been proposed regardless of the presence of a HARQ mechanism [START_REF] Cover | Capacity theorems for the relay channel[END_REF]- [START_REF] Nazer | Compute-and-Forward: Harnessing Interference Through Structured Codes[END_REF]. One can mention i) the orthogonal approach (where the source remains silent when the relay is active) with the strategy Amplify and Forward (AF), Decode-and-Forward (DF), etc., and more This work was supported by the Labex Digicosme PhD scholarship grant from Université Paris-Saclay.

interestingly ii) the non-orthogonal approach (where the source is still transmitting its packet when the relay is active) with the Slotted Amplify and Forward (SAF) [START_REF] Yang | Towards the Optimal Amplify-and-Forward Cooperative Diversity Scheme[END_REF] or the Nonorthogonal Decode-and-Forward (NDF) [START_REF] Guan | Opportunistic nonorthognal cooperative communications through decode-and-forward relaying[END_REF]. Note that, in NDF, even if the relay has correctly decoded the packet, it does not take over completely the message transmission since the source continues to broadcast the same message through other packets.

In contrast, only few works have considered jointly relay assisted transmission and HARQ. They usually assume halfduplex (HD) relays using a decode-and-forward strategy. In [START_REF] Chelli | On the Performance of Hybrid-ARQ with Incremental Redundancy and with Code Combining over Relay Channels[END_REF], a distributed Alamouti relaying scheme is investigated. Network coding approach for relay assisted HARQ has been developed in multi-user context as in [START_REF] Hong | Network-coding based HARQ scheme for mobile realy entworks[END_REF] where a linear combination of bits is sent by the relay when it has decoded and stored more than one packet not correctly received at the destination. In [START_REF] Larsson | Cooperative transmit diversity based on superposition modulation[END_REF], [START_REF] Chaitanya | Superposition Modulation Based Symmetric Relaying with Hybrid ARQ: Analysis and Optimization[END_REF], a superimposed modulation (linear combination of symbols) is proposed in multi-user context where a node transmits simultaneously its own data packet and the packet of another transmitter for which it acts as a relay. In [START_REF] Zhang | A new relay assisted Hybrid ARQ scheme[END_REF], [START_REF] Ma | A novel network coded relay-assisted Hybrid-ARQ scheme[END_REF], a new protocol in single-user context combining HARQ and DF relay is introduced. The idea is to let the source send a new message while the relay is retransmitting previous one. In both papers, this idea is only considered for a CC-HARQ with one retransmission credit. In addition only a Minimum Mean Square Error (MMSE) receiver is carried out for handling the interference between both simultaneous received messages at the destination. More precisely, in [START_REF] Zhang | A new relay assisted Hybrid ARQ scheme[END_REF], the authors considered an dynamic protocol where the source sends a new message rather than a space-time coded version of the previous message as soon as the received Signal-Interference-to-Noise Ratio (SINR) is higher than a pre-defined threshold. This implies i) that the source only seldom uses the ability to send a new message, and ii) that the source has the channel state information of the future channels. In [START_REF] Ma | A novel network coded relay-assisted Hybrid-ARQ scheme[END_REF], the authors considered only BPSK-modulated signals.

In both papers, the gain in throughput is marginal certainly due to the choice of the sub-optimal MMSE receivers. Note that the idea of sending more than one message simultaneously is close to the Multi-Packet reception in random access protocol as explained in [START_REF] Samano-Robles | A Random Access Protocol Incorporating Multi-packet Reception, Retransmission Diversity and Successive Interference Cancellation[END_REF].

The main contribution of this paper is to analyze the real impact of the protocol of [START_REF] Zhang | A new relay assisted Hybrid ARQ scheme[END_REF], [START_REF] Ma | A novel network coded relay-assisted Hybrid-ARQ scheme[END_REF] (the source sends a new message while the relay retransmits another one) in a more realistic setting: IR-HARQ, no channel state information at the transmitter, and better decoders. Indeed, we will show the gain in throughput of this protocol when the receiver is either optimally designed through information-theoretic tools (e.g., Multiple Access Channel -MAC-capacity region) or suboptimally chosen but using at least the Successive Interference Canceler (SIC) principle.

The remainder of the paper is organized as follows: In Section II, system model along with existing relay assisted HARQ schemes is presented. Proposed protocol, considered decoder as well its Markov chain model is drawn in Section III. Numerical results and comparison with existing protocols are provided in Section IV. Finally, Section V is devoted to concluding remarks. II. SYSTEM MODEL Consider a three nodes system with one source, one relay, and one destination. Each link (source-relay, sourcedestination, relay-destination) is modeled as a Rayleigh flat fading channel independent of the other ones. The coherence time of each link is equal to the time-slot duration containing N time-instants. Let h sr (m), h sd (m), and h rd (m) be the fading components for the source-relay, source-destination, and relay-destination links at the m-th time-slot respectively. The associated gains are

g sr (m) = |h sr (m)| 2 , g sd (m) = |h sd (m)| 2 , and g rd (m) = |h rd (m)| 2 with variance σ 2 sr = E[g sr (m)], σ 2 sd = E[g sd (m)], σ 2 rd = E[g rd (m)].
The relay is assumed to work in a half-duplex, decodeand-forward mode. After each time-slot, the relay and the destination broadcast an instantaneous error-free Acknowledgment (ACK) if they succeeded to decode their message or a Negative Acknowledgment (NACK) otherwise. Moreover perfect Channel State Information (CSI) at each receiver (relay or destination) is assumed available.

The sequence of messages to be transmitted by the source is denoted as m with ∈ N + . Each message contains N R information bits. In CC-HARQ, each message m is channel encoded with a rate R and modulated into a packet x of length N (equal to the time-slot duration). The packet is sent through a propagation channel at most C max times, thanks to the HARQ mechanism. In IR-HARQ, each message m is encoded via a mother code of rate R 0 and then punctured into C max codeword chunks denoted by d (c) with c ∈ {1, 2, . . . , C max }. The c-th codeword chunk is finally modulated into a packet of length N denoted as x (c) .

In presence of a relay, the performance depend on the forwarded packet. An efficient method [START_REF] Chelli | On the Performance of Hybrid-ARQ with Incremental Redundancy and with Code Combining over Relay Channels[END_REF] relies on the Alamouti space-time coding [START_REF] Alamouti | A simple transmit diversity technique for wireless communications[END_REF]. If the destination fails to decode the message after the c-th chunk and the relay succeeds to decode, the relay at the next time-slot sends the Alamouti-conjugate chunk

x(c+1) = [-x (c+1) ,2 , x (c+1) ,1 , -x (c+1) ,3 , • • • , x (c+1)
,N -1 ] assuming even N , while the source sends the chunk x

(c+1) if c + 1 ≤ C max .

III. PROPOSED PROTOCOL A. Protocol description

In our protocol, once the relay has decoded the message , hence is able to help the source by transmitting the appropriate chunks related to this message to the destination, the source trusts the relay in managing this message , and the source decides to send a new message in parallel. This protocol is expected to provide a higher throughput since two messages are sent simultaneously. However, the message error rate (MER) is also likely to be higher since at the destination, interference (one message is coming from the relay and another one from the source) occurs and degrades the detection. As a result, more transmissions are likely to occur, and one can hope that MER increase is small enough.

More precisely, assuming we are starting a protocol session, the source transmits sequence x (c) 1 , (c = 1, . . . , r), to the destination while the relay overhears the source transmission where r is the HARQ round from which the relay successfully decodes the message 1. At round r + 1, the relay transmits the sequence x (r+1) 1

, to the destination while the source transmits the first chunk of the next message, i.e., x

2 . The destination tries to decode both messages 1 and 2 simultaneously. A pair of ACK/NACK is sent to the relay and the source according to the success of decoding of each message. Let (N)ACK be the (non)acknowledgment message associated with the message .

• if ACK 1 /ACK 2 : the source sends x

(1)
3 , the relay overhears,

• if ACK 1 /NACK 2 : the source sends x (2)
2 , the relay overhears,

• if NACK 1 /ACK 2 : the source sends x

(if r + 2 ≤ C max , else the relay overhears), • if NACK 1 /NACK 2 : the source sends x (2) 2
and the relay transmits x (r+2) 1 (if r + 2 ≤ C max , else the relay overhears), and so on.

B. Decoder description

Assuming that the destination is receiving the t-th slot. The decoder relies on the set of observations O t given by the B max last slots, i.e., from t -B max + 1 to t. The contributions of the messages already decoded in previous slots are removed the observations. Then , the set M t corresponds to all the not yet decoded messages having at least one transmit packets within the observations set O t . Within M t , we select the subset of messages D t whose their first transmission is less old than D max slots. For instance, if a message has been sent at least once before the (t -D max + 1)-th slot, the message is considered to be delayed and we stop trying to decode it. Consequently, based on the observations O t , we have a Multiple Access Channel (MAC) where the messages to decode are D t and the other messages M t /D t are not to decode but are seen as a structured interference and not as a Gaussian noise. The performance of the decoder, i.e., which messages in D t have been successfully decoded, are then provided by the MAC capacity region since we assume capacity-achieving codes.

C. Theoretical analysis

We would like to exhibit the performance metrics (such as throughput and MER). Actually, we will see that the proposed protocol can be modeled as a Markov chain, and then the performance metrics will rely on the related transition probabilities [START_REF] Badia | Markov analysis of selective repeat type II hybrid ARQ using block codes[END_REF], [START_REF] Chen | A novel Markov-chain-based method for throughput analysis in truncated cooperative HARQ systems[END_REF]. Except otherwise stated, we assume C max = 2, B max = 2, and D max = 2 due to space limitation.

Hereafter we will i) describe the corresponding Markov chain, ii) characterize the transition probabilities (assuming decoders described in Section III-B), and iii) derive the throughput and MER based on these transition probabilities.

In Figs. 1234, we provide the 8 states of the Markov chain needed for describing the proposed protocol. Notice that even if only one time-slot, let's say m, is required for completely characterizing the states, they also provide information on the previous time-slot m-1 and the future one m+1. For instance, in S 1 and S 3 , x

+1 is necessarily sent at time-slot m + 1. In S 2 and S 4 , x

+2 is necessarily sent at time-slot m + 1. In S 5 , x (2) is necessarily sent at time-slot m + 1. In S 7 , the relay and the source send x (2) and x

+1 respectively at timeslot m + 1. In S 6 and S 8 , the source sends x (2) +1 at time-slot m + 1. Moreover, in S 2 , S 4 , S 6 , and S 8 , the system was in S 7 at time-slot m -1.

S D R ACK

x (1) or x Extension to any value C max is possible at the expense of the number of states. For instance, we succeeded to exhibit the states for C max = 3 and C max = 4 where their numbers are 19 and 49 respectively. Due to lack of space, we do not describe them here.

The transition matrix of the previous Markov chain is denoted by T = (t i,j ) (i,j)∈{1,••• ,8} 2 where t i,j the transition probability from S j to S i . We have 8 i=1 t i,j = 1. Except otherwise stated, t i,j = 0 for any i, j. Let P(Ω) be the probability of the event Ω. Consequently, we have t i,j = P(S i |S j ).

According to Bayes' rule, we get t i,j = q i,j p j with p j = P(S j ) and q i,j = P(S i , S j ).

When j = 1, • • • , 4, we get that t 1,j = P R < log 2 (1 + g sd (1)) , t 5,j = P(R > log 2 (1 + g sd (1)), R > log 2 (1 + g sr (1))),
and t 7,j = 1 -t 5,j -t 1,j .

When j = 5, we get that t 1,5 = q 1,5 /p 5 with

p 5 = P(R > log 2 (1 + g sd (1)), R > log 2 (1 + g sr (1)))
and

q 1,5 = P(R < log 2 (1 + g sd (1)) + log 2 (1 + g sd (2)), R > log 2 (1 + g sd (1)), R > log 2 (1 + g sr (1))).
Finally, t 3,5 = 1 -t 1,5 .

When j = 6, we obtain t 1,6 = q 1,6 /p 6 with

p 6 = P(R > log 2 (1 + g sd (0)), R < log 2 (1 + g sr (0)), R < log 2 (1 + g sd (0)) + log 2 1 + g rd (1) 1 + g sd (1) , R > log 2 (1 + g sd (1))
and

q 1,6 = P(R < log 2 (1 + g sd (1)) + log 2 (1 + g sd (2)), R > log 2 (1 + g sd (0)), R < log 2 (1 + g sr (0)), R < log 2 (1 + g sd (0)) + log 2 1 + g rd (1) 1 + g sd (1) , R > log 2 (1 + g sd (1)).
Finally, t 3,6 = 1 -t 1,6 . When j = 7, we have t 2,7 = q 2,7 /p 7 with

p 7 = P(R > log 2 (1 + g sd (1)), R < log 2 (1 + g sr (1)))
and

q 2,7 = P(R < log 2 (1 + g sd (2)), R < log 2 (1 + g sd (1)) + log 2 (1 + g rd (2)), 2R < log 2 (1 + g sd (1)) + log 2 (1 + g rd (2) + g sd (2)), R > log 2 (1 + g sd (1)), R < log 2 (1 + g sr (1))).
In order to obtain q 2,7 , we have remarked that the state S 2 deals with MIMO-Multiple Access Channel (MAC) whose the capacity region is provided in [START_REF] Goldsmith | Capacity limits of MIMO channels[END_REF]. We also have t 4,7 = q 4,7 /p 7 with

q 4,7 = P(R > log 2 (1 + g sd (1)) + log 2 1 + g rd (2) , R < log 2 1 + g sd (2) 1 + g rd (2) , R > log 2 (1 + g sd (1)), R < log 2 (1 + g sr (1))).
The term q 4,7 is obtained by remarking that once again we have a MIMO-MAC but the message coming from the relay is not correctly decoded while the message coming from the source is. Therefore the message coming from the source requires a rate smaller than the SIC corner point of the capacity region which justifies the ratio g sd (2)/(1 + g rd (2)) [START_REF] Bandemer | Simultaneous nonunique decoding is rate-optimal[END_REF]. In a similar way, we have t 6,7 = q 6,7 /p 7 with

q 6,7 = P(R < log 2 (1 + g sd (1)) + log 2 1 + g rd (2) 1 + g sd (2) , R > log 2 (1 + g sd (2)), R > log 2 (1 + g sd (1)), R < log 2 (1 + g sr (1))).
Finally, t 8,7 = 1 -t 2,7 -t 4,7 -t 6,7 .

When j = 8, we get t 1,8 = q 1,8 /p 8 with

p 8 = P(R > log 2 (1 + g sd (0)), R < log 2 (1 + g sr (0)), R > log 2 (1 + g sd (0)) + log 2 1 + g rd (1) 1 + g sd (1) , 2R > log 2 (1 + g sd (0)) + log 2 (1 + g rd (1) + g sd (1)), R > log 2 1 + g sd (1) 1 + g rd (1)
).

Moreover q 1,8 = q 1,8 + q 1,8 with where S 8 is the event described in p 8 . Finally, t 3,8 = 1 -t 1,8 . We remind the throughput is the average number of information bits correctly received at the destination per timeinstant. The MER is the average ratio of the number of dropped messages over the number of sent messages. We have

Throughput = R (π 1 + 2π 2 + π 4 + π 6 ) , (1)
MER = π 3 + π 4 + π 8 π 1 + π 2 + π 3 + π 4 + π 6 + π 8 . (2)
where π = [π 1 , • • • , π 8 ] denotes the steady state vector of the Markov chain related to the proposed protocol. This vector is computed by solving Tπ = π and forcing 8 k=1 π k = 1. In (1), π 2 is multiplied by 2 since S 2 leads to acknowledge two messages simultaneously.

IV. NUMERICAL RESULTS

We briefly illustrate numerically the interest of the proposed protocol. To do that, we consider • either capacity-achieving coding: the metrics (throughout and MER) are obtained according to (1)-( 2) where π is replaced with π computed by estimating the matrix T. In addition, we also simulate the HARQ mechanism according to the Markov chain's rule and count the number of correctly received packets to estimate the throughput and the MER. • or practical coding: IR-HARQ is implemented using Rate-Compatible Punctured Convolutional Codes (RCPC) of memory 4 and period 8 as defined in [START_REF] Hagenauer | Rate-compatible punctured convolutional codes and their applications[END_REF], and modulated by BPSK. The receiver yields Log Likelihood Ratio (LLR) for each message to each channel decoding. These LLR have been calculated assuming interference as a noise. Once the hard decision is made on the LLR, a SIC is applied in an iterative manner E b is the average energy consumed for sending one information bit, i.e., the energy consumed by the retransmission due to HARQ and relaying is taken into account. The relay is located halfway between the source and the destination.

In Fig. 5 we plot the throughput of no-relaying, Alamoutibased [START_REF] Chelli | On the Performance of Hybrid-ARQ with Incremental Redundancy and with Code Combining over Relay Channels[END_REF], and proposed protocols versus E b /N 0 for capacityachieving codes with C max = 2 and R = 0.8. The proposed protocol offers much higher throughput than existing ones especially for any SNR. This gain can be explained by the fact the source transmits new message while the relay still retransmits previous one and the interference is well managed through a capacity-achieving codes. Notice that the gain is much higher than those seen in [START_REF] Zhang | A new relay assisted Hybrid ARQ scheme[END_REF], [START_REF] Ma | A novel network coded relay-assisted Hybrid-ARQ scheme[END_REF], certainly due to the considered decoder. As a consequence, the protocol is powerful and so of great interest. In Fig. 6, we display MER of no-relaying, Alamouti-based [START_REF] Chelli | On the Performance of Hybrid-ARQ with Incremental Redundancy and with Code Combining over Relay Channels[END_REF], and proposed protocols versus E b /N 0 for capacityachieving codes with C max = 2 and R = 0.8. The proposed protocol has higher MER than the Alamouti-based protocol due to the interference at the destination between messages coming from the source and the relay. Nevertheless this loss in MER does not damage the throughput as seen in Fig. 5. In Fig. 7, we plot the throughput of no-relaying, Alamoutibased [START_REF] Chelli | On the Performance of Hybrid-ARQ with Incremental Redundancy and with Code Combining over Relay Channels[END_REF], and proposed protocols versus E b /N 0 for practical codes with C max = 2 and C max = 3. Once again, the proposed protocol outperforms the existing ones in terms of throughput. Once again, the gain is significant and higher as in the literature for medium and high SNR. Thus the SIC decoder instead of the MMSE one is crucial for such a protocol.

V. CONCLUSION

The proposed protocol, enabling the source to transmit new message while the relay retransmits the previous one, offered significant gain in throughput. Future work may focus on the power allocation between the source and the relay.

Fig. 1 :Fig. 2 :Fig. 3 :Fig. 4 :

 1234 Fig. 1: States S 1 (left) and S 2 (right)

q 1 , 8 =

 18 P(S 8 , R < log 2 (1 + g rd (1)), R < log 2 (1 + g sd (1)) + log 2 (1 + g sd (2)), 2R < log 2 (1 + g rd (1) + g sd (1)) + log 2 (1 + g sd (2))), and q 1,8 = P(S 8 , R > log 2 (1 + g rd (1)), R < log 2 1 + g sd (1) 1 + g rd (1) + log 2 (1 + g sd (2)))

Fig. 5 :

 5 Fig. 5: Throughput vs. E b /N 0 .

Fig. 6 :

 6 Fig. 6: MER vs. E b /N 0 .

Fig. 7 :

 7 Fig. 7: Throughput vs. E b /N 0 (practical coding).