Magali Zbinden
email: magali.zbinden@snv.jussieu.fr

Bruce Shillito

Nadine Le Bris

Constance De Villardi De Montlaur

Erwan Roussel

François Guyot

Françoise Gaill

Marie-Anne Cambon-Bonavita

New insigths on the metabolic diversity among the epibiotic microbial community of the hydrothermal shrimp Rimicaris exoculata

Keywords: high pressure experiments, hydrothermal vent shrimp, intracellular granules, iron, methane, sulfur

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Hydrothermal vent communities along the Mid-Atlantic Ridge (MAR) are dominated by large populations of caridean shrimps. Found in dense clusters of 40 000 individuals per m 3 [START_REF] Segonzac | L'énigme du comportement trophique des crevettes Alvinocarididae des sites hydrothermaux de la dorsale médioatlantique[END_REF], Rimicaris exoculata is the most abundant species on some of these sites. This shrimp has been found to host a dense bacterial epibiosis on the internal walls (branchiostegites) of its branchial chamber and on its mouthparts (scaphognathites and exopodites of the first maxillipeds) [START_REF] Van Dover | Feeding biology of the shrimp Rimicaris exoculata at hydrothermal vents on the Mid-Atlantic Ridge[END_REF][START_REF] Casanova | L'impact d'une épibiose bactérienne sur la morphologie fonctionnelle de crevettes associées à l'hydrothermalisme médio-Atlantique[END_REF][START_REF] Segonzac | L'énigme du comportement trophique des crevettes Alvinocarididae des sites hydrothermaux de la dorsale médioatlantique[END_REF][START_REF] Zbinden | Distribution of bacteria and associated minerals in the gill chamber of the vent shrimp Rimicaris exoculata and related biogeochemical processes[END_REF]. This indicates an intimate association between these organisms. The main source of dietary carbon could originate: 1) from bacteria ingested with the sulfide scraped from the chimney [START_REF] Van Dover | Feeding biology of the shrimp Rimicaris exoculata at hydrothermal vents on the Mid-Atlantic Ridge[END_REF], 2) from their epibiotic bacteria [START_REF] Segonzac | L'énigme du comportement trophique des crevettes Alvinocarididae des sites hydrothermaux de la dorsale médioatlantique[END_REF]Gebruk et al., 2000) or 3) from an autotrophic bacterial population living in the shrimp's gut [START_REF] Pond | Occurence of 16:2(n-4) and 18:2 (n-4) fatty acids in the lipids of the hydrothermal vent shrimps Rimicaris exoculata and Alvinocaris markensis: nutritional and trophic implications[END_REF][START_REF] Polz | Trophic ecology of massive shrimp aggregations at a mid-Atlantic Ridge hydrothermal vent site[END_REF][START_REF] Zbinden | Occurence of Deferribacterales and Entomoplasmatales in the deep-sea shrimp Rimicaris exoculata gut[END_REF]. Fatty acid abundances and carbon isotopic composition recently provided strong evidence that mature R. exoculata gain most of their carbon from the epibiotic bacteria within their carapace rather than from bacteria grazed on the chimney walls [START_REF] Rieley | Trophic ecology of Rimicaris exoculata: a combined lipid abundance/stable isotope approach[END_REF]. For shrimps sampled from the Snake Pit site, three bacterial morphotypes were described [START_REF] Segonzac | L'énigme du comportement trophique des crevettes Alvinocarididae des sites hydrothermaux de la dorsale médioatlantique[END_REF] which all belonged to the same phylotype of Epsilonproteobacteria [START_REF] Polz | Dominance of one bacterial phylotype at a Mid-Atlantic Ridge hydrothermal vent site[END_REF]. Although attempts to cultivate these microorganims failed until now, they were hypothesized to acquire their metabolic energy from sulfide oxidation [START_REF] Gebruk | Feeding specialization of bresiliid shrimps in the TAG site hydrothermal community[END_REF][START_REF] Wirsen | Chemosynthetic microbial activity at Mid-Atlantic Ridge hydrothermal vent sites[END_REF]. Chemosynthetic activity of the filamentous bacteria from the inner cephalothorax surface has been shown [START_REF] Wirsen | Chemosynthetic microbial activity at Mid-Atlantic Ridge hydrothermal vent sites[END_REF], but no significant increase of CO 2 incorporation was observed in the presence of reduced sulfur compounds [START_REF] Polz | Trophic ecology of massive shrimp aggregations at a mid-Atlantic Ridge hydrothermal vent site[END_REF].

More recently, [START_REF] Zbinden | Distribution of bacteria and associated minerals in the gill chamber of the vent shrimp Rimicaris exoculata and related biogeochemical processes[END_REF] suggested that another metabolic pathway, iron oxidation, could be involved at the iron-rich Rainbow ultramafic site. Unlike most active hydrothermal sites known to date, the hydrothermal circulation at Rainbow is hosted on mantle rocks. As a result, its fluid composition departs from the common range of hydrothermal end-members, and is relatively depleted in H 2 S and enriched in H 2 , FeII and CH 4 , as a result of the serpentinization processes [START_REF] Charlou | Geochemistry of high H 2 and CH 4 vent fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36°14'N, MAR)[END_REF][START_REF] Douville | The rainbow vent fluids (36°14'N, MAR): the influence of ultramafic rocks and phase separation on trace metal content in Mid-Atlantic Ridge hydrothermal fluids[END_REF].

During the ATOS cruise shrimps were all collected from the Rainbow site. The main objective of our work was to test the hypothesis that all the shrimp epibionts were sulfideoxidizers. To overcome the inhability to cultivate the epibionts, we performed in vivo experiments. For the first time, pressurized aquaria were used to gain information on the bacterial epibionts' metabolism. The aspect and ultrastructure of the bacteria were checked after incubations at 230 bars (in situ pressure), at 15°C (in situ temperature) with or without sulfide-enriched seawater (thereafter called sulfide pulses), and compared to in situ reference shrimps. A molecular survey was undertaken to get new insights on possible metabolic type of the epibiotic microbial communities of Rimicaris exoculata, particularly thiotrophy using the 5'-adenylylsulfate (APS) reductase gene.

Materials and methods

Animal collection and selection

Specimens of Rimicaris exoculata were collected during the French ATOS cruise (June 2001), on the Rainbow vent site (36°14.0' N, Mid-Atlantic Ridge, 2320 meter depth).

Shrimps were collected with the suction sampler of the ROV "Victor 6000", operated from the R/V "L'Atalante". Once on board, some live specimens were either immediately dissected into body components. These samples are referred to as "reference shrimps" further in the text. Alternatively, some shrimps were placed in pressure vessels (IPOCAMP™) for in vivo experiments (see below) and in this case dissected immediately after removal from the vessel. Scaphognathite samples were fixed in a 2.5% glutaraldehyde -sodium cacodylate buffered solution and later post-fixed in osmium tetroxide for morphological observations. Samples for X-ray analyses were not postfixed. For each treatment, shrimps in anecdysis were selected for observation according to the moult-staging method of [START_REF] Drach | Sur la méthode de détermination des stages d'intermue et son application générale aux Crustacés[END_REF], by examination of bristle-bearing appendages (uropods) under a lightmicroscope. The moulting stage was later confirmed by examination of the branchiostegite integument by light microscopy and Transmission Electron Microscopy (TEM). For molecular studies, shrimps were frozen immediately after recovery under sterile conditions. Once in the lab, the scaphognathites and branchiostegites were dissected and DNA extraction was performed.

Pressurized incubator IPOCAMP™

The stainless steel pressure vessel has an internal volume of approximately 19 liters (see [START_REF] Shillito | Temperature resistance of Hesiolyra bergi, a polychaetous annelid living on vent smoker walls[END_REF] for detailed description and diagrams). This is a flow-through pressure system, with flow rates that can reach 20 l.h -1 . Pressure oscillations arising from pump strokes (100 rpm) are less than 1 bar at working pressure. The temperature of the flowing seawater (filtered at 1 µm mesh) is constantly measured, at pressure, in the inlet and outlet lines (±1°C). Temperature regulation is powered by a regulation unit (Huber CC 240) that circulates ethylene-glycol through steel jackets surrounding the pressure vessel and around the seawater inlet line.

In vivo experiments. Re-pressurization at 230 bars was achieved in about 2 min after closure of the vessel. As the shrimps were sampled at the end of the dive, less than 2 h passed between the time the samples began decompression (submersible ascent) and the moment they were re-pressurized. At atmospheric pressure, just after the submersible recovery, the shrimps (except for some individuals, which may have been damaged by the suction sampler) were alive and active. Pressure vessel experiments were carried out at in situ pressure ( 230bars) and at 15°C, according to the literature data: 10-15°C [START_REF] Segonzac | L'énigme du comportement trophique des crevettes Alvinocarididae des sites hydrothermaux de la dorsale médioatlantique[END_REF] ; 3.8-14.7°C [START_REF] Zbinden | Distribution of bacteria and associated minerals in the gill chamber of the vent shrimp Rimicaris exoculata and related biogeochemical processes[END_REF] ; 13.2 ± 5.5°C [START_REF] Desbruyères | Variations in deep-sea hydrothermal vent communities on the Mid-Atlantic Ridge near the Azores plateau[END_REF]. Previous in vivo experiments showed a good physiological state of the shrimps when re-pressurized at these temperature and pressure conditions [START_REF] Ravaux | Heat-shock response and temperature resistance in the deep-sea vent shrimp Rimicaris exoculata[END_REF]. Only alive and active shrimps after treatment were used for the present study.

Two experiments at 230 bars were performed:

(1) Sample incubation at 15°C in surface seawater, to investigate the effect of depletion of electron donors on the shrimps and their epibionts. Twelve shrimps were placed in the pressure vessel, for 30 h. The seawater was regularly (5 times) renewed, by replacing a quarter of the total volume. Surface seawater oxygen level (253 µM) lies slightly above the concentration measured in the environment of the shrimps (Schmidt et al., in press). These samples are referred to as "non-sulfide shrimps" further in the text.

(2) Incubation at 15°C, with exposure to sulfide pulses. Nine shrimps were placed in the pressure vessel for 32 h. During the 32 h of the experiment, we first maintained the shrimps in normal sea-water for 8 hours. Then, 4 pulses were performed as follows : i) the inlet of the flow-through pressure system was fed with a reservoir containing 20 l of a solution of 25 µM sulfide in natural surface seawater. This concentration roughly corresponds to the maximum of estimated from the shrimps environment at Rainbow (Schmidt et al., in press). This moderate concentration also ensured that the oxygen is not fully depleted from the medium.

When the reservoir was almost empty, the outlet line was connected to the inlet line, in order to recirculate the sulfide-enriched seawater; ii) After an exposure of one hour, seawater was then pumped into the vessel for 2h ; iii) finally the vessel was closed for 3h before the next pulse started with a freshly prepared 25 µM sulfide solution. These samples are referred to as "sulfide shrimps" further in the text. The term "re-pressurised shrimps" englobes both "non sulfide" and "sulfide" shrimps.

Survival of the re-pressurized shrimps was determined at the end of the pressure experiments, by identifying each individual and witnessing its movements.

Light microscopy and transmission electron microscopy (TEM)

Samples were dehydrated in ethanol and propylene oxide series and then embedded in an epoxy resin (Serlabo). Semi-thin and ultra-thin sections were made on a Reichert-Jung Ultramicrotome (Ultracut E) using a diamond knife. Semi-thin sections were stained with toluidine blue for observations by light microscopy (using a Nikon Optiphot-pol microscope and a Zeiss Opton photomicroscope). For ultrastructural observations, thin sections were laid on copper grids and stained with uranyl acetate and lead citrate. Observations were carried out on a Philips 201 TEM, operating at 80 kV.

Energy dispersive X-ray microanalyses (EDX)

Microanalysis was carried out using a JEOL JEM 2100F transmission electron microscope, operating at 200 kV, and acquired with an energy dispersive X-ray detection system (Tracor 5400 FX), equipped with a Si(Li) diode, using a 2.4 nm probe.

Ultrastructural analyses and enumeration of bacteria

Exhaustive analysis and enumeration of bacteria and their intracellular granules were undertaken on one individual for each treatment. For each shrimp, bacteria associated to 5 setae of the scaphognathite were analyzed. For each seta, an overall picture was taken and picture of all the bacteria were then captured at a magnification of 20000. Bacteria cells were then counted and described. The occurrence of intracellular granules was noted for each cell.

Granules were defined as electron-dense spots larger than 1.5 mm on the pictures (i.e. 75 nm), as numerous dark spots of various sizes occur in the cells. Due to their small size, spots smaller than 75 nm cannot be analyzed by EDX and were not taken into account in this study because of the uncertainty on their nature.

Statistical analyses

A one-way ANOVA was used to test differences in the state of the bacteria (i.e. percentage of full granules) among treatments. Normality was judged visually from normal probability plots and homogeneity of variances was verified with the Levene test. A multiple range test using the Student-Newman-Keuls (SNK) procedure was performed to investigate the difference between treatments for significant results. All data analyses were carried out using Statistica v. 6 software.

DNA extraction

One in situ reference shrimp was dissected under sterile conditions. DNAs from scaphognathite (SC) and branchiostegite (LB), were extracted using the FastDNA SPIN kit for soil samples (Bio 101 System, Qbiogen) following the kit protocols.

PCR and cloning

PCR were performed using the universal primers for Bacteria or Archaea 16S rDNA on both (SC and LB) extracted DNA samples: E8F (AGA GTT TGA TCA TGG CTC AG) and U1492R (GTT ACC TTG TTA CGA CTT) for Bacteria and A8F (CGG TGG ATC CTG CCG GA) and A1492R (GGC TAC CTT GTT ACG ACT T) for Archaea. PCR cycles were as follows : 1 cycle of 3 min at 94°C, 30 cycles of 1 min at 94°C, 1 min 30 at 49°C and 2 min at 72°C and 1 cycle of 6 min at 72°C.

The gene encoding particulate methane monooxygenase subunit A (pmoA) was amplified on the SC DNA using the primers described by Duperron et al. (2007a) A189F ( GGN GAC TGG GAC TTC TGG ) and MB661R (CG GMG CAA CGT CYT TAC C ). PCR cycles were as follows : 1 cycle of 4 min at 92°C , 30 cycles of 1 min at 92°C, 1 min 30 at 55°C and 1 min at 72°C and 1 cycle of 9 min at 72°C.

The gene encoding the APS reductase gene was amplified on the SC DNA using the primers designed before (Blazejak et al., 2006). PCR cycles were as follows : 1 cycle of 4 min at 92°C , 30 cycles of 1 min at 92°C, 1 min 30 at 58°C and 1 min at 72°C and 1 cycle of 9 min at 72°C.

Approximately 100 ng of bulk DNA was amplified in a 50 µl reaction mix containing (final concentration) : 1X Taq DNA polymerase buffer (Q biogen Starsbourg, France), 2 µM of each dNTP, 20 µM of each primer and 2.5U of Taq DNA polymerase (Q Biogen France).

PCR products were then visualized on an agarose gel containing ethidium bromide before cloning. The PCR products were cloned with the TOPO TA Cloning kit (Invitrogen Corp., San Diego CA USA) following to the manufacturer's protocol. PCR products were purified using the QIAquick PCR purification kit (Qiagen SA, Grenoble, France) following the manufacturer's instructions. Clone libraries were constructed by transforming E. coli TOP10F'. Clones were selected on Petri dishes containing ampicilline (50µg/ml) and XGAL and IPTG for the white -blue selection. White clones were then cultured and treated for sequencing at the "Ouest Genopole Plateforme" (Roscoff, France, http//www.sbroscoff.fr/SG/) on a Abi prism 3100 GA (Applied Biosystem), using the Big-Dye Terminator V3.1 (Applied Biosystem) following the manufacturer's instructions.

Phylogenetic analyses

To determine approximate phylogenetic affiliations, sequences were compared to those available in databases using the BLAST network service [START_REF] Altschul | Basic local alignment search tool[END_REF]. Alignments of 16S rDNA sequences were performed using CLUSTALW [START_REF] Thompson | CLUSTAL W : improving the sensitivity of progressive multiple sequence alignment through sequence weighting, position-specific gap penalties and weight matrix choice[END_REF], further refined manually using SEAVIEW [START_REF] Galtier | SEAVIEW and PHYLO_WIN: two graphic tools for sequence alignment and molecular phylogeny[END_REF]. The trees were constructed by PHYLO-WIN [START_REF] Galtier | SEAVIEW and PHYLO_WIN: two graphic tools for sequence alignment and molecular phylogeny[END_REF]. Only homologous positions were included in the phylogenetic comparisons. For the 16S rDNA phylogenetic reconstruction, the robustness of inferred topology was tested by bootstrap resampling (500) [START_REF] Felsentein | Confidence limits on phylogenies: an approach using the bootstrap[END_REF] of the tree calculated on the basis of evolutionary distance (Neighbor-Joining-algorithm ; [START_REF] Saitou | The neighbor-joining method : a new method for reconstructing phylogenetic trees[END_REF] with Kimura 2 correction. Sequences displaying more than 97% similarity were considered to be related, and grouped in the same phylotype. Phylogenies of amino acid sequences of the pmoA (154 aa) and APS (129 aa) were reconstructed using PHYLO-WIN with Neighbor-Joining-algorithm and PAM distance (according to Dayhoff's PAM model).

The robustness of the inferred topology was tested by bootstrap resampling (500).

Nucleotide sequence accession numbers. Sequences have been deposited at EMBL with accession numbers: from AM412507 to AM412521 and from AM902724 to AM902731 for partial 16S rDNA sequences; from AM412502 to AM412506 for partial pmoA (particulate methane monooxygenase subunit A) gene; and from AM902732 to AM902736 for APS reductase gene.

Results

Morphology and ultrastructure of the epibionts

A total of 315 pictures was analyzed on which 6567 bacterial cells were counted. On in situ reference shrimps, TEM observations of the scaphognathite bacteria revealed more morphological diversity (figure 1) than previously described by Scanning Electron Microscopy (SEM) studies [START_REF] Segonzac | L'énigme du comportement trophique des crevettes Alvinocarididae des sites hydrothermaux de la dorsale médioatlantique[END_REF][START_REF] Zbinden | Distribution of bacteria and associated minerals in the gill chamber of the vent shrimp Rimicaris exoculata and related biogeochemical processes[END_REF].

We observed 3 types of filaments (two thin types and one large) and two types of rods.

Dimensions are in the range of those previously found (table 1). Two types of rods can be distinguished based on size, location and aspect of the intracellular contents. The first type (figure 1b) is characterized by short and thick cells, with a dense dark intracellular content.

They are mainly located on the setae. The second type (figure 1b) is longer and thinner, with a light intracellular content. These rods are mainly located on the barbula that emerge from the setae. Two types of thin filaments can be distinguished based on the aspect of the intracellular contents : i) a small number of thin filaments exhibit rectangular cells with no marked narrowing between two adjacent cells. Cells in these filaments show a homogeneous and dense content, with few electron light areas and no granules (figure 1d) ; ii) the others, more numerous, exhibit ovoid-shaped cells, with marked narrowing between two adjacent cells.

Cells of these filaments have a more heterogeneous intracellular content (which seems denser at the periphery and more diffuse in the center) and contain granules (figure 1e).

Ultrastructural changes are observed between the bacteria of re-pressurised shrimps and those of reference shrimps (figure 2). No significant morphological differences were noticed between the bacteria of the shrimps from both pressure experiments. Cells of large and thin filaments, as well as thick rods, have a less regular shape and exhibit a more heterogeneous intracellular content than those of reference shrimps (figure 2b-c). Only thin rods keep the ultrastructal aspect observed in reference shrimps. Some of the bacteria show a globular intracellular content (figure 2d) or additional membrane folds (figure 2e). These types are only observed among bacteria of the shrimps maintained at 230 bars. Occasionally, these morphotypes can have a very degraded aspect, with totally mis-shapen cells (figure 3a), completely globular cell contents (figure 3c) or cell ghosts (figure 3c). Cell ghosts are also occasionally observed among bacteria of reference shrimps where they represent 1.5 to 4% of all the bacteria, and may be due to the usual turn-over of the cells. Cells with irregular shape and contents account for up to 30% of all cells in the re-pressurised shrimps and ghosts up to 15% (intra-individual variation between the five setae is too high to test the significance of inter-individual variations and the effect of sulfide exposure). Furthermore, very few dividing cells were observed for re-pressurised shrimps, whereas they were numerous for in situ reference shrimps. Surprisingly we observed, for the first time among R. exoculata epibionts (in reference shrimps, as well as in re-pressurised ones), some bacteria with stacks of intracytoplasmic membranes typical of methanotrophs (figure 2f) in both reference and repressurised shrimps.

Intracellular electron dense granules

Only granules larger than 75 nm in diameter were considered, the largest measuring up to 200 nm. Spots under 75 nm were counted separately, as "spots". The number of granules and spots is higher for reference shrimps than for re-pressurised ones (table 2). Granules occurred only in one type of thin filament, and are absent from thick filaments and rods. A given cell may contain several granules and spots (up to 7 granules and 10 spots per cell).

In the reference shrimps, most of the granules appear full (i.e they are electron dense and appear black on micrographs, figure 4a), whereas most appear partially or completely empty for the re-pressurised shrimps (i.e they are electron light and appear, at least partly white on micrographs, figure 4b). Percentage of full granules for each experiment are illustrated on figure 5. The percentage of full granules differs significantly between reference and repressurised shrimps (one-way ANOVA test; F = 76.942, p < 10 -6 ), although no significant difference was detected between sulfide and non-sulfide shrimps at 230 bars (SNK a posteriori test, p > 0.05).

Chemical composition of granules

An EDX microanalysis was performed in order to determine the elemental composition of the granule content (figure 6). The control spectrum from the cytoplasmic area of the bacteria showed copper (Cu) peaks due to the support grid, uranyl (U) peaks due to uranyl acetate staining, and traces of chloride (Cl) due to the epoxy resin. Two types of granules were analyzed. The first type contains 2 main peaks : phosphorus (P) and iron (Fe), in some cases associated with small amounts of calcium (Ca) (not shown). The second type of granules shows a single peak of sulfur (S). Occasionally, traces of iron (Fe) are detected (but it can be due to the close occurrence of a thick iron oxide layer that surrounds some bacteria).

Preliminary screening of bacterial diversity

DNA was successfully extracted from scaphognathite and branchiostegite samples. PCR amplifications for Archaea failed regardless of the conditions tested, even with nested PCR.

For Bacteria, 69 clones were sequenced for the scaphognathite and 56 for the branchiostegite of an reference shrimp. Only 53 clones sequences were kept for the scaphognathite sample and 46 for the branchiostegite sample, the other clone sequences being too short or of bad quality. No chimera was detected in our study.

All the sequences are related to the Proteobacteria cluster (figure 7), mainly within the Epsilon and Gamma groups, the Alpha and Deltaproteobacteria being less abundant. One group of 19 sequences is related to the R. exoculata gut clone 15, found in a previous study on the gut of a specimen from the same vent site [START_REF] Zbinden | Occurence of Deferribacterales and Entomoplasmatales in the deep-sea shrimp Rimicaris exoculata gut[END_REF]. A second group of 13 sequences is related to sequences retrieved from a vent gastropod coming from Rodriguez Triple junction in the Indian Ocean [START_REF] Goffredi | Novel forms of structural integration between microbes and a hydrothermal vent gastropod from the Indian Ocean[END_REF]. A third group (5 clone sequences) is related to the Rimicaris exoculata epibiont [START_REF] Polz | Dominance of one bacterial phylotype at a Mid-Atlantic Ridge hydrothermal vent site[END_REF].

Nineteen clones sequences are related to the Rimicaris exoculata gut clone 22 [START_REF] Zbinden | Occurence of Deferribacterales and Entomoplasmatales in the deep-sea shrimp Rimicaris exoculata gut[END_REF]. Six clone sequences are related to the Deltaproteobacteria. Twenty four sequences are affiliated to the Gammaproteobacteria. These latter are related to sequences retrieved on a vent gastropod [START_REF] Goffredi | Novel forms of structural integration between microbes and a hydrothermal vent gastropod from the Indian Ocean[END_REF] and also to clone sequences retrieved on carbonate chimney from the Lost City vent field [START_REF] Brazelton | Methane-and sulfur-metabolizing microbial communities dominate the Lost City hydrothermal field ecosystem[END_REF]. The last group comprises eight clones, related to the Alphaproteobacteria, close to Marinosulfomonas methylotropha, and to a clone isolated from Lost City vent field [START_REF] Brazelton | Methane-and sulfur-metabolizing microbial communities dominate the Lost City hydrothermal field ecosystem[END_REF].

pmoA and APS sequence analyses

We successfully amplified the pmoA and APS reductase genes using DNA extracted from the scaphognathite. Fifteen clones were sequenced for the pmoA and 5 for the APS reductase. All the sequences were kept for the phylogenetic analyses. For the pmoA gene (Figure 8), two clone sequences are affiliated to the Methylobacter sp. group, two clones sequences are affiliated to a Bathymodiolus symbiont sequence and 11 clones sequences are affiliated to the Methylomonas methanica. For the APS reductase gene (Figure 9), 5 sequences were related to the Deltaproteobacteria. Ninety sequences were only marginally related to the Gammaproteobacteria APS gene (83% of similarity) and were related to the Idas thiotrophic clone (Duperron et al. 2007b).

As no genes, until now, of the iron-oxidation pathway for neutrophilic iron-oxidizing bacteria are known, this metabolic pathway cannot be investigated by this method.

Discussion

Is sulfide oxidation active in the epibiotic community ?

Transmission electron microscopy allowed us to refine the morphological descriptions of the epibionts on the reference shrimps, detecting two types of thin filaments, and two types of rods, in addition to the thick filaments. These results indicate that the morphological diversity of bacteria associated with R. exoculata is higher than previously reported (Casanova et al., 1993;[START_REF] Gebruk | Feeding specialization of bresiliid shrimps in the TAG site hydrothermal community[END_REF][START_REF] Zbinden | Distribution of bacteria and associated minerals in the gill chamber of the vent shrimp Rimicaris exoculata and related biogeochemical processes[END_REF]. The molecular survey supports this result. Even though additionnal sequence investigations are needed to fully describe the microbial diversity within the gill chamber, the present study provides a preliminary overview of the epibiotic community composition. Many Epsilonproteobacteria sequences are related to microbial diversity usually associated with various hydrothermal invertebrates (Alvinella pompejana: [START_REF] Alain | Phylogenetic characterization of the bacterial assemblage associated with the hydrothermal vent polychaete Paralvinella palmiformis[END_REF]Paralvinella palmiformis: Alain et al., 2004;gastropods: Goffredi et al., 2004;[START_REF] Suzuki | Novel chemoautotrophic endosymbiosis between a member of the epsilonproteobacteria and the hydrothermal-vent gastropod Alviniconcha aff. hessleri (Gastropoda: Provannidae) from the Indian Ocean[END_REF] and Rimicaris exoculata gut: [START_REF] Zbinden | Occurence of Deferribacterales and Entomoplasmatales in the deep-sea shrimp Rimicaris exoculata gut[END_REF] and to the MAR environment [START_REF] Lopez-Garcia | Wide bacterial diversity associated with tubes of the vent worm Riftia pachyptila[END_REF]. Only five sequences are slightly related to "Rimicaris exoculata ecto-epibiont". The Deltaproteobacteria diversity is restricted to one cluster, and is related to an uncultured bacterium colonizing the mineral surfaces of a sulfide-microbial incubator. These microorganisms are usually thought to play a role in the sulfur cycle. In addition, we obtained APS reductase gene sequences that are related to those of the Desulfobulbaceae [START_REF] Friedrich | Phylogenetic analysis reveals multiple lateral transfers of adenosine-5'phosphosulfate reductase genes among sulfate-reducing microorganisms[END_REF] known to be thiotroph. Most of the APS gene sequences obtained were related to the Idas thiotrophic symbiont gene (Duperron et al., 2007b), which is a Gammaproteobacteria, but with a low level of similarity (83%). In our phylogenetic survey, we did not obtain any 16S rDNA gene sequence related to thiotrophic Gammaproteobacteria, so it is unlikely that our APS gene sequences are related to these Gammaproteobacteria. As no Epsilonproteobacteria APS gene sequence is available in databanks, our APS gene sequences are more likely related to the numerous Epsilonproteobacteria identified in the phylogenetic survey. It is noteworthy that the APS gene can be transferred laterally among Bacteria. It is therefore not a good phylogenetic marker [START_REF] Friedrich | Phylogenetic analysis reveals multiple lateral transfers of adenosine-5'phosphosulfate reductase genes among sulfate-reducing microorganisms[END_REF][START_REF] Meyer | Molecular analysis of the diversity of sulfate-reducing and sulfur-oxidizing prokaryotes in the environment using aprA as functional marker gene[END_REF].

Bacteria associated with re-pressurised shrimps exhibit different ultrastructures compared to the reference shrimps. A mean of 30% of the epibionts display what we interpret as a degraded aspect (i.e. heterogeneous or globular cellular content, irregular wall shapes, cell ghosts). In addition, the number of dividing cells is higher for the reference shrimps, indicating a better physiological state. These results could indicate that some of the bacteria cannot withstand the chemical environment of the re-pressurisation experiments, whether or not sulfides are present.

TEM observations of the epibionts reveal the massive occurrence of intracellular granules.

Such granules are often present in prokaryotic organisms [START_REF] Shively | Inclusion bodies in prokaryotes[END_REF]. They comprise polyglucoside, polyphosphate granules, crystals or paracrystalline arrays such as magnetosomes (Fe 3 O 4 ), poly-ß-hydroalkanoate (PHA) and sulfur globules. The main roles of these granules are hypothesized to be storage forms of energy and/or of various compounds such as carbon, sulfur and phosphates. They can also play a part in detoxification processes.

X-ray analyses indicate that there are two type of granules, one type containing phosphorus (P) and iron (Fe), most probably under polyphosphate form; the other type containing mainly sulfur (S). Several granules can occur in one bacterial cell, but they are always of the same type. The maintenance in a pressurized aquarium lead to the emptying of most of the granules, which suggests a storage role. Addition of sulfide does not affect this emptying phenomenon. However, the granules were counted as a whole, as it was no longer possible to morphologically distinguish the polyphosphate from the sulfur granules. It is conceivable that the slightly higher percentage of full granules, counted in the bacteria that received sulfide pulses (see figure 5), is due to a better conservation of the sulfur granules. R. exoculata epibionts (from the Snake Pit site) were hypothesized to acquire their metabolic energy from sulfide oxidation. At the ultrastructural level, sulfur-oxidizing bacteria are characterized by the accumulation of large granules of elemental sulfur, which is known to dissolve in solvents like those commonly used for classical TEM preparations [START_REF] Vetter | Elemental sulfur in the gills of three species of clams containing chemoautotrophic symbiotic bacteria: a possible inorganic energy storage compound[END_REF]. Consequently, these globules appear empty in thin sections [START_REF] Lechaire | In situ localization of sulphur in the thiotrophic symbiotic model Lucina pectinata (Gmelin, 1791) by cryo-EFTEM microanalysis[END_REF]. On our sections, the granule contents were not removed during preparation steps, which suggests that they are not elemental sulfur under the form usually found in sulfur-oxidizing bacteria. We can then hypothesize that these granules are rather formed of another type of more stable cristalline sulfur or are sulfur-rich organic matter. Nevertheless, sulfur-containing biopolymers are rare : they are mostly proteins containing methionine and cysteine, or complex polysaccharides that contain sulfate groups. PTE (polythioester), a new class of sulfur-containing polymer, have recently been described, [START_REF] Lütke-Eversloh | Identification of a new class of biopolymer : bacterial synthesis of a sulfur-containing polymer with thioester linkages[END_REF]. It belongs to the polyhydroxyalkanoates (PHAs), a class of biopolymers known to occur abundantly as storage compounds for energy and carbon, in a large variety of bacteria and archaea [START_REF] Anderson | Occurence, metabolism, metabolic role, and industrial uses of bacterial polyhydroxyalkanoates[END_REF]).

Taken all together, the TEM observations of bacteria associated to re-pressurised shrimps show a low positive impact of sulfide reexposure. Three hypotheses could thus be put forward to explain this: 1) the concentration and frequency of the pulses were insufficient to allow a good maintenance of the epibionts, or 2) these bacteria do not all rely on sulfide for their growth, or 3) the chemical composition of the fluid in the pressure vessel was not adapted for epibiont growth that may require more complex substrates as suggested by the lack of cultures despite many attempts. Considering the results of previous work on the epibionts of R. exoculata [START_REF] Zbinden | Distribution of bacteria and associated minerals in the gill chamber of the vent shrimp Rimicaris exoculata and related biogeochemical processes[END_REF] and the chemistry of this peculiar environment : low sulfide but high iron and methane concentration [START_REF] Charlou | Geochemistry of high H 2 and CH 4 vent fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36°14'N, MAR)[END_REF][START_REF] Douville | The rainbow vent fluids (36°14'N, MAR): the influence of ultramafic rocks and phase separation on trace metal content in Mid-Atlantic Ridge hydrothermal fluids[END_REF], it is possible that some bacteria do not rely on sulfide oxidation but rather on iron or methane oxidation.

Occurrence of iron oxidation among the epibiotic community

Genes involved in iron oxidation at neutral pH are still unknown and iron oxidizers show a broad diversity among the Proteobacteria [START_REF] Edwards | Isolation and characterization of novel psychrophilic, neutrophilic, Fe-oxidizing, chemolithoautotrophic a-and g-Proteobacteria from the deep-sea[END_REF]. So, iron oxidation metabolism could not be studied through a molecular approaches. Nevertheless, iron polyphosphate granules were detected inside the epibiont cells. Polyphosphate granules are widely distributed in prokaryotes, ranging in diameter from 48 nm to 1µm [START_REF] Shively | Inclusion bodies in prokaryotes[END_REF].

Putative roles of polyphosphate are numerous : ATP substitute, energy storage or chelator of metal ions [START_REF] Kornberg | Inorganic polyphosphate : toward making a forgotten polymer unforgettable[END_REF]. [START_REF] Lechaire | Elemental characterization of microorganism granules by EFTEM in the tube wall of a deep-sea vent invertebrate[END_REF] described the occurrence of iron polyphosphates granules in bacteria associated with the tube of Riftia pachyptila, a hydrothermal vent vestimentiferan. Since polyphosphates are known to fluctuate in response to nutritional and other parameters, these authors suggest that they could act as a reservoir of oxygen in the case of environmental anoxia. As the occurrence of iron-oxidizers among the bacteria has been suggested [START_REF] Zbinden | Distribution of bacteria and associated minerals in the gill chamber of the vent shrimp Rimicaris exoculata and related biogeochemical processes[END_REF], these granules could be a reservoir for iron. Alternatively, if these granules occur in non-iron oxidizing bacteria, the chelation of iron by the polyphosphate granules could reduce its toxicity for the cell.

Anyway, the only way to certify the occurrence of iron-oxidizing bacteria among the epibionts is to successfully cultivate and isolate these strains. Such attempts are under progress in our lab.

A possible alternative metabolism : methanotrophy and methylotrophy

A sixth morphotype, bacteria with stacks of intracytoplasmic membranes typical of type I methanotrophs, was observed for the first time among R. exoculata epibionts. Moreover, our sequences cluster with known Gammaproteobacteria methanotrophic epibionts sequences, such as Bathymodiolus methanotrophic gill symbionts [START_REF] Duperron | Dual symbiosis in a Bathymodiolus sp. mussel from a methane seep on the Gabon continental margin (Southeast Atlantic): 16S rRNA phylogeny and distribution of the symbionts in gills[END_REF]. This is also supported by our three groups of pmoA sequences that clearly belong to the methylotrophic Gammaproteobacteria class (Methylomonas sp., Methylobacter sp. and Bathymodiolus pmoA gene sequences). In addition, some clone sequences are related to Alphaproteobacteria methylotroph species and to Epsilonproteobacteria clone sequences retrieved from enrichedmethane environments such as the MAR Lost City and Rainbow sites, or to the Milano mud volcano (Figure 7).

Co-occurrence of different metabolic types in the epibiotic community

Taken all together, our microscopic observations and molecular data seem to indicate that at least three metabolic types could co-occur among the epibiotic microbial community associated to R. exoculata at Rainbow: iron-oxidation, methanotrophy and thiotrophy. [START_REF] Desbruyères | Variations in deep-sea hydrothermal vent communities on the Mid-Atlantic Ridge near the Azores plateau[END_REF] tried to correlate biological diversity to the varying composition of end-member fluids. According to the amount of iron oxide closely associated to the epibionts [START_REF] Zbinden | Distribution of bacteria and associated minerals in the gill chamber of the vent shrimp Rimicaris exoculata and related biogeochemical processes[END_REF], and to the high level of ferrous iron in the pure fluids [START_REF] Charlou | Geochemistry of high H 2 and CH 4 vent fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36°14'N, MAR)[END_REF], we suggest that iron oxidation may be the dominant metabolism for this site. Recently, [START_REF] Salerno | Characterization of symbiont populations in life history stages of mussels from chemosynthetic environments[END_REF] correlated the relative microbial abundance of epibiont types of two species of mussels (Bathymodiolus azoricus and B. heckerae) with the availability of CH 4 and dissolved H 2 S in the end-member fluids. They found that when the CH 4 :H 2 S ratio was less than 1 (as for Snake Pit, [START_REF] Campbell | The chemistry of springs on the Mid-Atlantic Ridge[END_REF] then thiotrophic epibionts were dominant. If the ratio was greater than 2 (as for Lost City, [START_REF] Kelley | An off-axis hydrothermal vent field near the Mid-Atlantic Ridge at 30[END_REF] then methanotrophs were the dominant epibionts. For Rainbow, the ratio of CH 4 :H 2 S varies from 1.54 to 2.61 in pure fluids [START_REF] Charlou | Geochemistry of high H 2 and CH 4 vent fluids issuing from ultramafic rocks at the Rainbow hydrothermal field (36°14'N, MAR)[END_REF]. Applying the [START_REF] Salerno | Characterization of symbiont populations in life history stages of mussels from chemosynthetic environments[END_REF] empirical model to Rimicaris epibionts at Rainbow, would suggest that methanotrophy is an important metabolic pathway, possibly dominating sulfide oxidation. Sampling and in situ measurements in shrimp swarms provide nevertheless a more realistic picture of the environmental conditions experienced by the shrimps. A recent study on potential electron donors for microbial primary production within the swarms at Rainbow indicates that ferrous iron is the most favorable energy source to support epibiotic growth. Methane and sulfide would appear as secondary energy sources in this environment, where hydrogen could also represent an altenative energy source for the epibionts (Schmidt et al., in press).

Conclusion

Based on TEM observations, and a preliminary molecular survey, the diversity of the Rimicaris exoculata epibionts (in terms of morphology and metabolism) appears to be higher than previously reported. Based on these results, we propose that the three metabolic types (iron, sulfur and methane oxidation) co-occur within the epibiont biomass associated with Rimicaris exoculata, and that the relative contribution of each metabolism may differ according to the local fluid chemical composition. A much wider scale study, with animals collected from chemically contrasted environments, is needed to better understand the connections of the epibiotic bacterial communities in response to the chemistry of the environment.

Figure legends

Rimicaris exoculata clone SCAII15

Rimicaris exoculata clone SC16S37

Rimicaris exoculata clone LB16S07

Rimicaris exoculata clone SCA16S42

Rimicaris exoculata clone LB16S22

Rimicaris exoculata clone LB16S31

Rimicaris exoculata clone LB16S14

Rimicaris exoculata clone LBI32

Rimicaris exoculata clone SC16S40

Rimicaris exoculata clone SCAII29

Figure 1 :

 1 Figure 1: Bacteria associated with a scaphognathite seta of a reference shrimp. a) General

Figure 2 :

 2 Figure 2: Bacteria associated with a scaphognathite seta of the re-pressurised shrimps. a)

Figure 3 :

 3 Figure 3: Evolution of the morphotypes observed in the re-pressurised shrimps. Filament

Figure 4 :

 4 Figure 4: Bacterial intracellular granules. Granules are full (arrows) in bacteria associated

Figure 5 :

 5 Figure 5: Percentage of full granules in bacteria according to treatment. Diagram showing the

Figure 6 :

 6 Figure 6: Elemental X-ray microanalyzes of the bacterial intracellular granules. Spectra were

Figure 7 :

 7 Figure 7: Phylogenetic trees obtained using Neighbor-Joining analysis with bootstrap

Figure 8 :

 8 Figure 8: Neighbor-Joining tree of pmoA amino acid sequences from Rimicaris exoculata

Figure 9 :

 9 Figure 9: Neighbor-Joining tree of APS reductase amino acid sequences from Rimicaris

  Figure 1 Click here to download high resolution image

  Figure 7

Table 1 :

 1 Cell sizes of the various bacterial morphotype observed (values are given in µm and correspond to the upper values measured).

		Cell diameter	Cell height
	Large filament	5,5	2,45
	Thin filament (1)	1,1	2,35
	Thin filament (2)	1,5	2,75
	Thick rods (type 1)	0,6	1,25
	Thin rods (type 2)	0,3	3

Table 1

 1

Table 2 :

 2 Total numbers of bacteria analyzed, with number of granules and spots for each treatment.

		Bacterial
			Granules Spots
		cells
	Reference shrimps	1574	721	875
	Non-sulfide shrimps	3110	911	219
	Sulfide shrimps	1883	628	207

Table 2

 2

Acknowledgements. The authors wish to thank P.M. Sarradin, chief scientist of the ATOS cruise, as well as the captain and crew of the R/V Atalante and the Victor ROV team. The authors also thank Eric Thiébaut for his help with the statistical analyses, and Philippe Compère for his help in determination of the moulting stages. The author are also grateful to

Stephane Hourdez for his review of the manuscript. Electron microscopy was performed at the Service de Microscopie Electronique, IFR 83 de Biologie Integrative-CNRS/Paris VI. This work was partly funded with the help of the MOMARNET and VENTOX (EVK3 CT-1999-0003) programs, Ifremer research institute and Région Bretagne and Ouest Génopole.


Matthieu Arzel
email: matthieu.arzel@telecom-bretagne.eu

Cyril Lahuec

Member, IEEE Christophe Jego
email: christophe.jego@ims-bordeaux.fr

Senior Member, IEEE Warren J Gross
email: wjgross@ece.mcgill.ca

Yvain Bruned
email: yvain.bruned@eleves.bretagne.ens-cachan.fr

Stochastic Multiple Stream Decoding of Cortex Codes

Keywords: Cortex codes, stochastic decoding, Sum-Product algorithm

Cortex codes are short length block codes having a large Hamming distance. Their modular construction, based on simple and very short block codes, yield to difficulties in efficiently decoding them with digital decoders implementing the Sum-Product algorithm. However, this construction lends itself to analog decoding with performance close to ML decoding as was recently demonstrated. A digital decoding method close to analog decoding is stochastic decoding. This paper brings the two together to design a Cortex stochastic architecture with good decoding performance. Moreover, the proposed stochastic decoder architecture is simplified when compared to the customary one. Instead of edge or tracking forecast memories the proposed architecture uses multiple streams to represent the same probability and deterministic shufflers. This results in a more efficient architecture in terms of ratio between data throughput and hardware complexity. Finally, the proposed method offers decoding performance similar to a Min-Sum decoder with 50 iterations.

I. INTRODUCTION

Turbo [START_REF] Berrou | Near shannon limit error-correcting coding and decoding: turbo codes[END_REF] and LDPC [START_REF] Gallager | Low-density parity-check codes[END_REF], [START_REF] Mackay | Near shannon limit performance of low density parity check codes[END_REF] codes allow near optimal decoding performance for codes of block lengths larger than a few hundreds of bits. However, these code families are not adapted to smaller blocks. Also based on iterative encoding and interleaving stages, Cortex codes [START_REF] Carlach | A new family of block turbo codes[END_REF], [START_REF] Carlach | A new scheme for building good self-dual block codes[END_REF] were invented for this purpose.

They are asymptotically good [START_REF] Olocco | A family of self-dual codes which behave in many respects like random linear codes of rate[END_REF] and possess interesting properties such as a systematic construction of self-dual codes [START_REF] Carlach | A new family of block turbo codes[END_REF] and the possibility to associate every type-II self dual code with a Cortex code [START_REF] Otmani | Codes cortex et construction de codes auto-duaux optimaux[END_REF].

Although the Cortex construction offers short codes with large Hamming distances, they are generally difficult to decode with usual digital implementation techniques [START_REF] Otmani | Codes cortex et construction de codes auto-duaux optimaux[END_REF], [START_REF] Cadic | Construction de turbo codes courts possédant de bonnes propriétés de distance minimale[END_REF] due to the complexity of the decoding graphs and the large number of hidden variables.

The first efficient Cortex decoder was implemented for codes based on the (4,2,2) Hadamard code with analog circuits [START_REF] Perez-Chamorro | Decoding a family of dense codes using the sum-product algorithm[END_REF] applying the Sum-Product Algorithm (SPA). But is it possible to achieve such results with digital circuits? The state-of-the-art digital implementations of the original SPA for LDPC codes consist of different optimized versions of the Min-Sum solution provided in [START_REF] Fossorier | Reduced complexity iterative decoding of low-density parity check codes based on belief propagation[END_REF], with the exception of stochastic circuits originally proposed in [START_REF] Gaudet | Iterative decoding using stochastic computation[END_REF]. Stochastic decoders have been so optimized that they provide some of the most efficient implementations of LDPC decoders [START_REF] Tehrani | Majority-based tracking forecast memories for stochastic LDPC decoding[END_REF].

Principles of stochastic computation were elaborated in the 1960's [START_REF] Gaines | Stochastic computing[END_REF], [START_REF] Poppelbaum | Stochastic computing elements and systems[END_REF] as a method to carry out complex operations with a low hardware complexity. The probabilities are converted into streams of stochastic bits using Bernoulli sequences in which the information is given by the statistics of the bit streams. Complex arithmetic operations on probabilities such as multiplication and division are transformed into operations on bits using elementary logic gates. Stochastic decoder architectures are designed with low computational complexity and a high level of parallelism [START_REF] Gross | Stochastic implementation of LDPC decoders[END_REF] [16] achieving high throughputs [START_REF] Tehrani | Majority-based tracking forecast memories for stochastic LDPC decoding[END_REF], [START_REF] Sharifi Tehrani | Fully parallel stochastic LDPC decoders[END_REF], [START_REF] Tehrani | Tracking forecast memories in stochastic decoders[END_REF]. Moreover, stochastic decoding is of high interest for low-power decoders [START_REF] Gaudet | Switching activity in stochastic decoders[END_REF] and fault-tolerant nanoscale circuits [START_REF] Winstead | A probabilistic LDPC-coded fault compensation technique for reliable nanoscale computing[END_REF].

The main goal of this paper is to show that Cortex codes can be efficiently decoded, despite the complexity of their decoding graphs, by state-of-the-art techniques, i.e. stochastic processing. An original idea is also introduced to reduce the number of clock cycles required to decode one codeword and to replace the Edge Memories (EMs) [START_REF] Sharifi Tehrani | Fully parallel stochastic LDPC decoders[END_REF] by simple deterministic shufflers.

The paper is organized as follows. Section II summarizes the principles of Cortex codes. A stochastic decoder architecture is presented to deal with them in Section III. This architecture is then compared with analog SPA and digital Min-Sum counterparts in terms of decoding performance in Section IV. Section V concludes the paper.

C 0 0 C 0 1 C 0 i C 0 p-1 C 1 0 C 1 1 C 1 i C 1 p-1 C s-1 0 C s-1 1 C s-1 i C s-1 p-1 C s 0 C s 1 C s i C s p-1 v 0 0 v 0 p×m-1 v 1 0 v 1 p×m-1 v s-1 0 v s-1 p×m-1 x 0 x j x m-1 x m x m+j x 2m-1 x i×m x i×m+j x (i+1)×m-1 x (p-1)×m x (p-1)×m+j x p×m-1 r 0 r j r m-1 r m r m+j r 2m-1 r i×m r i×m+j r (i+1)×m-1 r (p-1)×m r (p-1)×m+j r p×m-1 Π 0 Π 1 Π s-1
Fig. 1: Cortex encoder made up of s interleaving stages and (s + 1) × m component encoders.

II. CORTEX CODES

A. Design principles

Cortex codes were originally designed as systematic codes of rate one half [START_REF] Carlach | A new family of block turbo codes[END_REF]. As shown in Fig. 1, the systematic symbols are grouped in frames of k symbols denoted by x i . Any frame x is sliced into p parts of same length m. Each sub-frame, or slice, is independently encoded using a component encoder C 0 j of rate one half. The resulting redundant symbols are grouped into a frame of length k denoted by v 0 .

Then, this frame is interleaved over its full-length k. This slicing-encoding-grouping-interleaving scheme is iterated s times. Finally, the resulting frame v s is again sliced and encoded to yield the redundant frame r of length k. If the same self-dual code is used for any component code, then, depending on constraints on the interleavers [START_REF] Carlach | A systematic construction of self-dual codes[END_REF], the resulting Cortex code is also self-dual. Thus, codes with Hamming distances multiple of two or four are built. Using this Cortex construction, many known and new extremal short codes can be built, as shown in [START_REF] Otmani | Codes cortex et construction de codes auto-duaux optimaux[END_REF].

B. C4 codes

Whereas the Cortex codes generally used the extended [START_REF] Cadic | Construction de turbo codes courts possédant de bonnes propriétés de distance minimale[END_REF][START_REF] Carlach | A new family of block turbo codes[END_REF][START_REF] Carlach | A new family of block turbo codes[END_REF] Hamming code as component code, other codes can be used. For instance, in [START_REF] Perez-Chamorro | Decoding a family of dense codes using the sum-product algorithm[END_REF] the basic (4,2,2) Hadamard code, the smallest self-dual code, was proposed as component code with a simplified Tanner graph as illustrated in Fig. 2.

The resulting Cortex codes are referred to as C4 codes. Moreover, instead of constraining the design of Cortex codes with a reduced number of interleaving stages (one or two) as advised by [START_REF] Olocco | A family of self-dual codes which behave in many respects like random linear codes of rate[END_REF], Perez-Chamorro showed in [START_REF] Perez-Chamorro | Analogue decoding of the cortex codes[END_REF] that Cortex codes with more stages (up to six) have good decoding performance.

x 0

x 1 r 0 r 1
Fig. Fig. 3: BER performance of the (32,16,8) Cortex code provided in [START_REF] Otmani | Codes cortex et construction de codes auto-duaux optimaux[END_REF] and in [START_REF] Perez-Chamorro | Analogue decoding of the cortex codes[END_REF].

III. DIGITAL DECODER DESIGN

A. Choice of a case study (32,16,8) Cortex codes have been built using different component codes and interleaving stages. First, three stages of [START_REF] Cadic | Construction de turbo codes courts possédant de bonnes propriétés de distance minimale[END_REF][START_REF] Carlach | A new family of block turbo codes[END_REF][START_REF] Carlach | A new family of block turbo codes[END_REF] Hamming codes were proposed and digitally decoded with a floating-point SPA in [START_REF] Otmani | Codes cortex et construction de codes auto-duaux optimaux[END_REF]. Second, six stages of (4,2,2) Hadamard codes were introduced and decoded by means of an analog SPA decoder in [START_REF] Perez-Chamorro | Analogue decoding of the cortex codes[END_REF]. Obtained from behavioral simulations, the Bit-Error Rate (BER) performance of both solutions is given in Fig. 3. Note that Perez-Chamorro's solution outperforms Otmani's one by 1.7dB at BER=10 -5 , because of the girth of the decoding graph equal to 6 in the former case and equal to 4 in the latter case. Therefore, this code is chosen as case study for the proposed stochastic decoding method.

B. Cost of solving the latching problem

A C4 code can be decoded with the SPA by means of a stochastic architecture made up of random number generators (RNGs) and elementary logic gates as described in [START_REF] Sharifi Tehrani | Fully parallel stochastic LDPC decoders[END_REF]. One major problem in stochastic decoding which deeply degrades the performance is known as the latching problem [START_REF] Winstead | Stochastic iterative decoders[END_REF]. It is related to the sensitivity to the level of random switching activity [START_REF] Winstead | Error-control decoders and probabilistic computation[END_REF], which is especially critical at high Signal-to-Noise Ratios (SNRs). Different solutions have been suggested to solve the latching problem, and thus, to improve the BER performance of stochastic decoding, such as: using supernodes [START_REF] Winstead | Stochastic iterative decoders[END_REF],

scaling the received Log-Likelihood Ratios (LLRs) up to a maximum value [START_REF] Winstead | Error-control decoders and probabilistic computation[END_REF], Edge Memories (EMs)

A B C 32-bit EM 5 ADR[4:0] I 1 I 2 O s 0 s 1 s 2 s 3 s 4 s 5 s 6 s 7 s 8 s 9
Fig. 4: EM-based architecture with probabilities represented by single stochastic streams and processed by logic units connected through Edge Memories.

insertion and Noise-Dependent Scaling (NDS) [START_REF] Sharifi Tehrani | Fully parallel stochastic LDPC decoders[END_REF]. Basically, these solutions aim at re-randomizing and decorrelating stochastic streams.

An EM is a complex unit based on a register in which only valuable bits referred to as regenerative bits, i.e. avoiding signals stuck at '0' or '1', are written and randomly read. Such a unit is efficient to solve the latching problem when the register depth is sufficient (typically between 32 and 64) and when it is duplicated for any vertex of the decoding graph, as detailed in [START_REF] Tehrani | Tracking forecast memories in stochastic decoders[END_REF]. Thus, EMs are costly in terms of silicon area. To improve that, some alternatives have been proposed such as the Tracking Forecast Memory (TFM) [START_REF] Tehrani | Tracking forecast memories in stochastic decoders[END_REF] and the Majority-based TFM (MTFM) [START_REF] Tehrani | Majority-based tracking forecast memories for stochastic LDPC decoding[END_REF]. A TFM-based decoder was shown to require 40% of the ASIC area of an EM-based decoder with no performance loss. The resulting circuits were shown in [START_REF] Tehrani | Majority-based tracking forecast memories for stochastic LDPC decoding[END_REF], [START_REF] Sharifi Tehrani | Fully parallel stochastic LDPC decoders[END_REF], [START_REF] Tehrani | Tracking forecast memories in stochastic decoders[END_REF] to be competitive fully parallel decoders in terms of architecture efficiency (data throughput over circuit area). Nevertheless, this optimized solution still requires 8-bit registers, random address generators, adders and comparators.

Re-randomizing and decorrelating stochastic streams can be done without these complex units if all the probabilities are represented by multiple stochastic streams that can be shuffled, as explained in the next section.

C. Multiple stream architecture

An EM-based architecture is illustrated in Fig. 4. Each probability P i is carried by a stochastic stream s i and is processed with other probabilities by a logic unit -A, B or C -or an EM to avoid latching.

This EM picks up a regenerative bit from a pool when correlation occurs. It is also possible to pick up a regenerative bit from another independent stochastic stream representing the same probability. To reduce the correlation between the concurrent streams, more than two are required. Moreover, the regenerative bit has to be randomly selected among them. Thus, the EM-based architecture in Fig. (a) Multiple stream architecture. Number Generators (RNGs) and comparators as detailed in [START_REF] Gaudet | Iterative decoding using stochastic computation[END_REF]. To simplify further the architecture, the shuffling rule can be deterministic to avoid additional RNGs, for instance circularly shifting bits of one position to the left at each DC.

J K J K J K J K S J K S J K J K S 1 0 1 0 J K S Barrel-Shifter I 2 [0 : 3] I 1 [0 : 3] I 1 [0] I 1 [0] I 2 [0] X[0] X[0] O[0] T [0] I 1 [3] I 1 [3] I 2 [3] X[3] X[3] O[3] T [3] CLK V [0 : 3] T [0 : 3] O[0 : 3] (
In addition, representing a probability by p stochastic streams instead of one divides the number of DCs by p to insure the same precision. Thus, this novel architecture has a throughput similar to any other stochastic architecture parallelized at degree p as suggested in [START_REF] Gaudet | Iterative decoding using stochastic computation[END_REF]. Therefore, the multiple stream architecture has to be compared to state-of-the-art solutions in terms of architecture efficiency, i.e. ratio between throughput and hardware complexity, as done in the next sections.

D. Stochastic multiple stream Sum-Product decoder

The proposed stochastic processing mimics that of the analog decoder in [START_REF] Perez-Chamorro | Decoding a family of dense codes using the sum-product algorithm[END_REF], i.e. the decoding is based on the encoding graph. Input data feed the decoding graph in which all the vertices are, as conventionnaly, bidirectionnal. Messages are exchanged along these vertices until the decoder converges and stops. Given the encoding graph of a Cortex code (Fig. 1), Fig. 6 illustrates the architecture of a Cortex decoder using the

Π Π Π -1 Π -1
Fig. 6: Stochastic cortex decoder made up of a ROM, a serial-to-parallel memory and a fully parallel multiple stream stochastic core.

proposed multiple stream processing. The channel outputs are converted into symbol probabilities thanks to a ROM and parallelized to feed a stochastic computation core. This fully parallel core is composed of three types of units: converters from fixed-point probabilities into multiple stochastic streams (FX2MS units), bidirectional stochastic decoders of (4,2,2) Hadamard codes (C4Dec, C4FB and C4B units) and interleavers (Π and Π -1 ). The C4B modules compute the messages sent to the C4FB modules on their left-hand side using the redundant information. The C4Dec modules compute the messages needed by the C4FB modules on their right-hand side using the systematic information. In addition, these modules take the decision on the decoded bits. The C4FB modules computes the messages needed by their left and right-hand side neighbors. This last module is detailed in Fig. 7a. All the interconnections are p-bit buses processed in parallel by the logic gates. For instance each p-bit XOR has two p-bit inputs and one p-bit output and is made up of p conventional XORs (each one has two 1-bit inputs and one 1-bit output).

A C4B module is half a C4FB one. The C4Dec and the C4B modules are similar except the former requires two 3-bit counters to provide decisions on the received codeword as illustrated in Fig. 7b. Figures 7a and7b present the components required by the exact computing. Some flip-flops may be added to reduce the critical path, without any performance loss.

IV. SIMULATION RESULTS

Three digital decoder behavioral models were written in C language to assess the decoding performance of the three decoding methods, namely the proposed 16-stream stochastic decoder, a conventional

f s 2×i f s 2×i+1 f s+1 Π -1 (2×i) f s+1 Π -1 (2×i+1) b s+1 Π(2×i) b s+1 Π(2×i+1) x 2×i
x 2×i+1 (b) C4Dec module. Fig. 7: Stochastic multiple stream processing modules computing forward/backward messages and decisions. All the shuffler inputs V , which give the shifting value and are driven by the same signal, are not mentioned. stochastic decoder with 32-bit EMs and a Min-Sum decoder using the flooding schedule and fixed-point 8-bit messages. Note that an iteration consists of updating all the edges of the decoding graph once.

A. Decoding performance

As shown in Fig. 8a, the 16-stream decoder with shufflers outperforms by 0.1dB the conventional stochastic decoder with 32-bit EMs and requires twenty times fewer DCs. Moreover, the 16-stream decoder achieves the BER performance of the 50-iteration Min-Sum decoder.

To achieve high throughput with adapted buffering, the decoding terminates when the decoded frame is a codeword or when a maximum number of DCs is reached. As shown in Fig. 8b, the amount of DCs needed to achieve this criterion depends on the signal-to-noise ratio and on the stochastic decoder used.

Actually, while the 32-bit EM-based decoder requires many dozens of DCs to decode up to 90% of the frames, the 16-stream solution decodes 90% of the frames in less than ten DCs . This is correlated with the high ratio (90%) of regenerative bits feeding the shufflers within a few DCs while the EM-based decoder produces 90% of regenerative bits after many dozens of DCs, as illustrated in Fig. 8c.

These results confirm stochastic computation as a practical approach for decoding Cortex codes and multiple stream decoding a promising innovation. However, reducing the number of DCs by a factor of twenty with a BER improvement is not a sufficient metric to fully assess the efficiency of the proposed decoding solution, the circuit complexity and the achievable data throughput must also be compared.

B. Architecture efficiency

The 16-stream decoder with shufflers is compared with a stochastic decoder with 32-bit EMs. First, the efficiencies of the input fixed-point-to-stochastic-stream modules -FX2MS in the multiple stream architectures -has to be assessed. For any FX2MS of the 16-stream decoder, sixteen random bits are generated over one DC. This is sixteen times as complex as generating one random bit over one DC as done by any equivalent FX2SS module of a conventional stochastic decoder. However, since any [START_REF] Carlach | A new family of block turbo codes[END_REF] DRAFT Second, the stochastic core is made of C4FB, C4B and C4Dec modules with either parallel logic gates and shufflers or simple logic gates and 32-bit EMs. The C4FB module of the former architecture requires seven percent less of logic gates than the C4FB module of the latter and runs twenty times less DCs.

Moreover, many random bits have to be generated for the EMs whereas the shufflers do not require any. Naturally, efficient architectures as a distributed one [START_REF] Sharifi Tehrani | Fully parallel stochastic LDPC decoders[END_REF] have been proposed to generate random bits. Nevertheless, the hardware resources cost for providing random numbers is still high. Thus, the proposed multiple stream stochastic C4FB is about twenty and ten times as efficient as EM-based and TFM-based cores, respectively. However, any C4Dec module has to accumulate one stream per output bit in a single-stream scheme and 16 streams in a 16-stream scheme. The latter requires so many adders that a 16-stream C4Dec is three times as complex as an EM-based single-stream C4Dec, and is finally 20/3 times as efficient. The total amount of random bits and logic gates required to decode C4 codewords of length 2 × k with s interleaving stages was assessed and is given in Tab. Ia. If no stopping criterion is used for the (32,16,8) code with s = 5, the 16-stream architecture requires 3.9 times as many random bits and 1.6 times as many logic gates and 1/20 times as many DCs as an EM-based architecture. If the processing is stopped when the decoded frame is a codeword, then the mean DC number depends on the signal-to-noise ratio and can be reduced down to a few DCs as shown in Tab. Ib. In any case, the 16-stream decoder is the most efficient solution. Indeed, the hardware usage is between five and twelve times as efficient with a 16-stream decoder as with an EM-based decoder. Compared to a TFM-based decoder, the proposed architecture is two to five times as efficient. Thus, the multiple stream architecture offers the best efficiency for the implementation of stochastic Cortex decoders. A TFM-based ASIC LDPC decoder [START_REF] Tehrani | Tracking forecast memories in stochastic decoders[END_REF] was designed for the ST Microelectronics 90nm process, and clocked at 400MHz. Assuming a similar clock frequency, the 16-stream Cortex decoder can provide a data throughput of 64Mb/s if no stopping criterion is used and up to 1.9Gb/s @ 7dB with a stopping criterion and adapted buffering. If a Cortex Min-Sum decoder could be clocked at 300MHz, as a recent 65nm Min-Sum ASIC decoder is [START_REF] Zhong | Area-efficient min-sum decoder design for high-rate quasi-cyclic low-density parity-check codes in magnetic recording[END_REF], it would process data at 14Mb/s at fifty iterations, with no performance loss, and 34 Mb/s at twenty iterations, with a loss larger than 0.3dB if no stopping criterion is used. Even with a single iteration, this Min-Sum decoder could not operate at more than 680 Mbit/s. Based on these considerations and since previous stochastic architectures were already serious challengers to conventional digital decoders [START_REF] Sharifi Tehrani | Fully parallel stochastic LDPC decoders[END_REF],

it can be concluded that the multiple stream stochastic architecture is the most valuable solution for a digital ASIC implementation of an iterative Cortex decoder based on the belief-propagation algorithm.

V. CONCLUSION

An innovative stochastic architecture using multiple streams and deterministic shufflers has been proposed to digitally decode Cortex codes proposed by Perez-Chamorro in [START_REF] Perez-Chamorro | Analogue decoding of the cortex codes[END_REF]. Compared to stochastic decoders using single streams and Edge Memories or TFMs, the proposed stochastic architecture presents the best architecture efficiency defined as the ratio between data throughput and circuit area. Thus, Cortex codes are optimal short codes which can be built and digitally decoded with good BER performance with a belief-propagation algorithm. In the case of a (32,16,8) C4 code, the architecture efficiency of a multiple stream decoder is up to five times as large as the one achieved using state-of-the-art techniques, i.e.

with TFMs. Moreover, this multiple stream design could be applied to design LDPC decoders or turbo decoders with some possible architecture-efficiency improvements.

  4 can be replaced by the multiple stream architecture shown in Fig. 5b where all the streams and the logic gates are duplicated p times (p>2) and the random bit selection is done by a simple shuffler illustrated in Fig. 5b. The shuffler

Fig. 5 :

 5 Fig. 5: Novel architecture with probabilities represented by four stochastic streams and processed by parallel logic units connected through shufflers.

  sum C4 decoding (20 iterations, 8-bit inputs) Digital Min-sum C4 decoding (50 iterations, 8-bit inputs) Stochastic C4 decoding (32-bit EMs, 2000 DCs, 8-bit inputs) Stochastic C4 decoding (16 streams, 100 DCs, 8-bit inputs)(a) BER performance. Ratio of frames decoded within a given number of DCs by stochastic decoders using a stopping criterion. Ratio of regenerative bits at the inputs of the EMs or of the shufflers.

Fig. 8 :

 8 Fig. 8: Performance comparison of 32-bit EM-based and 16-stream decoders for a (32,16,8) Cortex code.

TABLE I :

 I Comparison of stochastic Cortex decoders in terms of (a) hardware resources for codewords of length 2× k and s interleaving stages and of (b) mean number of DCs required at different Eb/N0s before stopping. These numbers of DCs include the initializing phase of one DC. The processing is stopped when the decoded frame is a codeword or the maximum number of DCs is reached.

		(a)			(b)
	Random bits Logic gates (normalized count)	32-bit EM-based k× (26+10×(s-1)) k× (1.2 + (s -1))	16-stream k × 256 k× (3.5+0.9×(s-1))	Eb/N0 5dB 6dB	DC mean for a 32-bit EM-based (up to 2000DCs) 62.5 32.9	DC mean for a 16-stream (up to 100DCs) 6.2 4.4
				7dB	17.2	3.3
	16-stream FX2MS run one twentieth of the clock cycles required by any conventional counterpart, the
	16-stream architecture improves the efficiency by a ratio of 20/16.

[START_REF] Carlach | A new family of block turbo codes[END_REF] DRAFT