Michael Danger
email: danger@univ-metz.fr

J Uli E N Cornut

A RN AUD ELGER § , -A ND Eric C Hau Ve T †

Julien Cornut

Effects of burial on leaf litter quality, microbial conditioning and palatability to three shredder taxa

Keywords: aquatic fungi, hyporheic zone, leaf litter stoichiometry, organic matter breakdown, shredder growth rate

1. Heterotrophic microorganisms are crucial for mineralising leaf litter and rendering it more palatable to leaf-shredding invertebrates. A substantial part of leaf litter entering running waters may be buried in the streambed and thus be exposed to the constraining conditions prevailing in the hyporheic zone. The fate of this buried organic matter and particularly the role of microbial conditioning in this habitat remain largely unexplored. 2. The aim of this study was to determine how the location of leaf litter within the streambed (i.e. at the surface or buried), as well as the leaf litter burial history, may affect the leaf-associated aquatic hyphomycete communities and therefore leaf consumption by invertebrate detritivores. We tested the hypotheses that (i) burial of leaf litter would result in lower decomposition rates associated with changes in microbial assemblages compared with leaf litter at the surface and (ii) altered microbial conditioning of buried leaf litter would lead to decreased quality and palatability to their consumers, translating into lower growth rates of detritivores. 3. These hypotheses were tested experimentally in a second-order stream where leaf-associated microbial communities, as well as leaf litter decomposition rates, elemental composition and toughness, were compared across controlled treatments differing by their location within the streambed. We examined the effects of the diverse conditioning treatments on decaying leaf palatability to consumers through feeding trials on three shredder taxa including a freshwater amphipod, of which we also determined the growth rate. 4. Microbial leaf litter decomposition, fungal biomass and sporulation rates were reduced when leaf litter was buried in the hyporheic zone. While the total species richness of fungal assemblages was similar among treatments, the composition of fungal assemblages was affected by leaf litter burial in sediment. 5. Leaf litter burial markedly affected the food quality (especially P content) of leaf material, probably due to the changes in microbial conditioning. Leaf litter palatability to shredders was highest for leaves exposed at the sediment surface and tended to be negatively related to leaf litter toughness and C ⁄ P ratio. In addition, burial of leaf litter led to lower amphipod growth rates, which were positively correlated with leaf litter P content. 6. These results emphasise the importance of leaf colonisation by aquatic fungi in the hyporheic zone of headwater streams, where fungal conditioning of leaf litter appears particularly critical for nutrient and energy transfer to higher trophic levels.

Introduction

Low-order forested streams, where light limitation restricts primary production, rely upon the input of plant organic matter from the riparian zone to fuel in-stream processes [START_REF] Vannote | The river continuum concept[END_REF]. Therefore, their metabolism is primarily heterotrophic with carbon and energy flow from coarse particulate organic matter (CPOM) to the stream food web being mediated by microorganisms [START_REF] Ba ¨rlocher | Hyphomycetes as intermediaries of energy flow in streams[END_REF][START_REF] Gessner | Importance of stream microfungi in controlling breakdown rates of leaf litter[END_REF][START_REF] Suberkropp | Microorganisms and organic matter processing[END_REF][START_REF] Grac | The role of invertebrates on leaf litter decomposition in streams -a review[END_REF][START_REF] Hieber | Contribution of stream detritivores, fungi, and bacteria to leaf breakdown based on biomass estimates[END_REF]. A large quantity of this organic matter input is stored in the hyporheic zone of streams after its burial during storms [START_REF] Herbst | Effects of burial on food value and consumption of leaf detritus by aquatic invertebrates in a lowland forest stream[END_REF] or flooding [START_REF] Metzler | Storage and dynamics of subsurface detritus in a sandbottomed stream[END_REF][START_REF] Naegeli | POM-dynamics and community respiration in the sediments of a floodprone prealpine river (Necker, Switzerland)[END_REF]. Despite the hyporheic zones of streams having long been recognised as sustaining many biotic and abiotic processes [START_REF] Orghidan | Ein neuer Lebensraum des unterirdischen Wassers: der hyporheische Biotop[END_REF][START_REF] Williams | The occurrence of benthos deep in the substratum of a stream[END_REF][START_REF] Gibert | Surface water-groundwater ecotones[END_REF][START_REF] White | Perspectives on defining and delineating hyporheic zones[END_REF], the specific significance of such processes in the whole stream functioning has long been neglected. Most studies on the dynamics of organic matter in streams have been limited to benthic habitats, with processes occurring above the streambed surfaces [START_REF] Kaushik | The fate of the dead leaves that fall into streams[END_REF][START_REF] Webster | Vascular plant breakdown in freshwater ecosystems[END_REF]. As underlined by [START_REF] Boulton | River ecosystem health down under: assessing ecological condition in riverine groundwater zones in Australia[END_REF], these lotic ecosystems were at that time only considered as conducting water, solutes and OM from the catchment downstream, without considering other flow paths above or below the ground where constant exchanges of water and materials occur. The few authors who have attempted to determine the fate of leaf litter once incorporated into stream sediments have generally reported a reduction in rates of leaf litter decomposition [START_REF] Reice | Environmental patchiness and the breakdown of leaf litter in a woodland stream[END_REF][START_REF] Herbst | Effects of burial on food value and consumption of leaf detritus by aquatic invertebrates in a lowland forest stream[END_REF][START_REF] Rounick | Leaf processing in 2 contrasting beech forest streams -effects of physical and biotic factors on litter breakdown[END_REF][START_REF] Metzler | Storage and dynamics of subsurface detritus in a sandbottomed stream[END_REF][START_REF] Naamane | The breakdown of leaves of poplar and holm oak in three Moroccan streams: effect of burial in the sediment[END_REF][START_REF] Cornut | Early stages of leaf decomposition are mediated by aquatic fungi in the hyporheic zone of woodland streams[END_REF], even though ambiguous or less welldefined patterns have also been observed [START_REF] Mayack | Effects of burial and floodplain retention on stream processing of allochthonous litter[END_REF][START_REF] Smith | The breakdown of buried and surface-placed leaf-litter in an upland stream[END_REF]. Overall, the ecological significance of leaf litter decomposition in the hyporheic zone for headwater stream metabolism remains poorly documented. [START_REF] Cornut | Early stages of leaf decomposition are mediated by aquatic fungi in the hyporheic zone of woodland streams[END_REF] have recently examined how the location of leaf litter within the streambed, either at the surface or buried, may affect the leaf-associated decomposer communities and leaf litter degradation. Their findings indicate that burial within the substratum reduces the litter breakdown rate by limiting the access of invertebrate detritivores to leaves, suggesting a potential major role of fungi like aquatic hyphomycetes. Fungal colonisation results in increased leaf litter nutritional value and palatability to shredding invertebrates through fungal biomass and associated changes in leaf tissue because of their enzymatic activity [START_REF] Rounick | Leaf processing in 2 contrasting beech forest streams -effects of physical and biotic factors on litter breakdown[END_REF][START_REF] Grac | Patterns and processes in detritus-based stream systems[END_REF]). Shredders seem to prefer feeding on leaves with certain characteristics, such as high nitrogen (N) content, low levels of structural or secondary leaf compounds and a high degree of fungal colonisation [START_REF] Schlief | Palatability of leaves conditioned in streams affected by mine drainage: a feeding experiment with Gammarus pulex (L.)[END_REF]. The enhancement of leaf detritus food quality by fungi has been shown to affect the lifehistory traits of shredders such as growth, survivorship and reproduction [START_REF] Suberkropp | Effects of aquatic fungi on feeding preferences and bioenergetics of Pycnopsyche gentilis (Trichoptera: Limnephilidae)[END_REF]. [START_REF] Herbst | Effects of burial on food value and consumption of leaf detritus by aquatic invertebrates in a lowland forest stream[END_REF] first reported that burial within the sediment depressed the consumption rates of leaves by shredders compared with those incubated at the streambed surface. This response was suggested to be related to the higher crude protein content of surface-incubated leaves. Other hypotheses have also been proposed, including differences in leaf toughness or the intensity of microbial colonisation. Because of the scarcity of literature on the subject, the role of aquatic hyphomycetes in the conditioning of leaves within the hyporheic zone and its consequences in terms of palatability to shredder and leaf decomposition rate remain largely unknown.

Improvement in the elemental composition of resources through fungal activity is recognised as a main driver of nutrient transfer efficiency in food webs, affecting in turn a wide range of ecological processes [START_REF] Cebrian | Patterns in the fate of production in plant communities[END_REF][START_REF] Sterner | Ecological Stoichiometry: The Biology of Elements From Molecules to the Biosphere[END_REF]. Phosphorus (P) and nitrogen (N) are often limiting elements for the growth and activity of microbial decomposers in many ecosystems [START_REF] Elser | Growth rate-stoichiometry couplings in diverse biota[END_REF] and particularly in streams [START_REF] Rosemond | Landscape variation in phosphorus concentration and effects on detritus-based tropical streams[END_REF][START_REF] Cross | Consumer-resource stoichiometry in detritus based streams[END_REF]. Leaf litter nutrient content has been shown as positively altering shredder consumption rates in headwater streams [START_REF] Irons | Consumption of leaf detritus by a stream shredder: influence of tree species and nutrient status[END_REF]). Yet, the relationship between leaf litter nutrient contents and growth rates of shredding invertebrate in these ecosystems has been far less examined.

The aim of the present study was to determine how the location of leaf litter within the streambed (i.e. at the surface or buried), as well as the leaf litter burial history, may affect the leaf-associated aquatic hyphomycete communities and leaf consumption by invertebrate detritivores. Burial of leaf litter should result in lower decomposition rates associated with changes in microbial assemblages compared with leaf litter at the surface. Consequently, altered microbial conditioning of buried leaf litter should lead to decreased quality and palatability to their consumers, translating into lower growth rates of detritivores. We tested experimentally these hypotheses in a second-order stream, where the leaf-associated fungal community, and the leaf decomposition rate, elemental composition, and consumption by three common shredder taxa were compared across four treatments regarding the effects of leaf burial and history of exposition to the benthic and hyporheic zones. Consequences of these treatments on invertebrate growth rate were determined for one amphipod species.

Methods

Study sites

The field site was located in the Alzeau, a second-order stream (3.5-4.7 m wide, 0.30 m deep, mean discharge c. 0.5 m 3 s )l ) in the Montagne Noire (south-western France; 02°13¢23¢¢E, 43°25¢51¢¢N; elevation 743 m a.s.l). The area is surrounded by a mixed broadleaf forest dominated by alder, Alnus glutinosa (L.) Gaertn, and oak, Quercus petraea (Mattus.) Liebl., and is subject to a mountainous climate. The study was conducted from January to May 2009 in a pool-riffle-pool sequence, extending over c. 100 m, similar to those described by [START_REF] Cornut | Early stages of leaf decomposition are mediated by aquatic fungi in the hyporheic zone of woodland streams[END_REF]. Four representative riffles were selected, each riffle being considered as a replicate site for leaf exposition. To identify downwelling and upwelling areas in the hyporheic zone, vertical hydraulic gradients (VHGs) were measured from the equation VHG (m m )1 ) = Dh ⁄ Dl, where Dh = h stream ) h piezometer and Dl is the distance between the streambed and the top of a Plexiglas minipiezometer screen [START_REF] Baxter | Measuring groundwater-stream water exchange: new techniques for installing minipiezometers and estimating hydraulic conductivity[END_REF]. The sediment was unconsolidated and mostly made of coarse particles (35% of particles being superior to 5 mm in diameter). The average hydraulic conductivity through the sediment of the four riffles reached 22 cm h )1 . Stream water temperatures were recorded every 2 h throughout the experiment using calibrated data loggers (SmartButton, ACR Systems Inc., BC, Canada). Water chemistry was determined on seven dates, at the beginning of the experiment and then on every sampling date. Water sampling was carried out on the four replicate sites, both at the surface of the sediment and within the hyporheic zone at 15 cm below the sediment surface. In the hyporheic zone, water was sampled using a hand-held vacuum pump immersed in a Plexiglas minipiezometer.

Conductivity, pH and dissolved oxygen concentrations were measured in the field using portable instruments (pH-meter 320i and Oxi 330i, WTW, Weilheim, Germany; Conductimeter Dist, HANNA, Woonsocket, RI, U.S.A.). Water samples were filtered in the field using GF ⁄ F filters (Glass fibre filters, Whatman, Clifton, NJ, U.S.A.; nominal cut-off 0.7 lm) and stored at 4 °C in pre-rinsed polyethylene bottles until analyses in the laboratory. Concentrations of PO 4 -P, measured as soluble reactive phosphorous (SRP), and NO 3 -N were determined using standard colorimetric methods [START_REF] Afnor | Eaux-Me ´thodes d'Essais[END_REF].

Leaf litter conditioning and mass loss

Oak was selected as a slow decomposing leaf species and with a particularly low palatability in the absence of microbial colonisation. Oak leaves were collected at abscission using a suspended net in the riparian zone of the Alzeau river in autumn 2008. About 2.5 g (±0.02 g) of air-dried leaves was enclosed in fine (0.5-mm) nylon mesh bags, 10 • 10 cm sized. The fine mesh excluded most invertebrates without interfering with microbial colonisation [START_REF] Boulton | A review of methodology used to measure leaf litter decomposition in lotic environments: time to turn over a new leaf[END_REF].

A total of 144 litter bags were introduced into the stream in mid-January 2009, following four conditions that simulate different scenarios after leaf litter introduction into a stream: (i) strictly benthic (B), that is, leaf litter exposed at the surface of the sediment throughout the experiment; (ii) benthic-hyporheic (BH), that is, leaf litter exposed at the surface of the sediment for 19 days allowing inoculation by and initial development of benthic microorganisms, then buried into the sediment until the end of the experiment; (iii) hyporheic-benthic (HB), that is, leaf litter directly buried into the sediment, then exposed at the surface of the sediment after 19 days; and (iv) strictly hyporheic (H), that is, leaf litter buried in the sediment throughout the experiment. Hyporheic leaf bags were buried at 15-20 cm depth into the sediment using a small shovel. In the selected stream, some shredder taxa (mainly Leuctra spp. and to a lesser extent Sericostoma) were found to occur at this depth and thus be able to access buried leaf litter and be directly affected by differences in leaf litter palatability [START_REF] Cornut | Early stages of leaf decomposition are mediated by aquatic fungi in the hyporheic zone of woodland streams[END_REF]. The experiment lasted 117 days, and one litter bag of each treatment was randomly sampled from each of the four replicate riffles at six dates (after 7, 19, 35, 56, 82 and 117 days) to follow leaf conditioning and decomposition. In addition, after 35, 56 and 82 days, one supplementary litter bag was randomly sampled for each treatment from each of the four riffles to determine the leaf palatability to three shredder taxa. Each sampled litter bag was stored individually in plastic zip-lock bag and brought back to the laboratory at 4 °C. Then, leaves were quickly washed individually to remove small sediments until processing for diverse analyses and consumption measurements. For each sample, a set of 12 leaf discs of 12 mm diameter was cut from which five discs were stored at )18 °C until ergosterol determinations and seven used to quantify the spore production by aquatic hyphomycetes. The remaining leaf material was stored at )18 °C until being freeze-dried and weighted. It was then ground using a bead-grinder (Culatti, Zurich, Switzerland), and aliquots of 300-400 mg were combusted at 450 °C for 5 h to estimate leaf ash-free dry mass (AFDM). Leaf litter decomposition rate was determined from ratios of remaining to initial leaf AFDM.

Microbial colonisation of leaves and litter quality

At each sampling date, several parameters were followed to estimate the leaf litter microbial colonisation and quality for consumers. To estimate the fungal diversity in leaves, seven freshly cut leaf discs were quickly placed in glass Petri dishes filled with 20 mL of pre-filtered (GF ⁄ F, Whatman, nominal cut-off: 0.7 lm) stream water. Dishes were gently agitated in the dark on an orbital shaker (60 rpm, 25.4-mm orbital path) at 10 °C for 48 h to stimulate the production of fungal asexual spores. Thereafter, spore suspensions were transferred into 50-mL polyethylene tubes, the Petri dish and leaf discs were rinsed with distilled water to collect spores no longer in suspension, and the volume was adjusted to 35 mL with 2 mL of 37% formalin and distilled water. The leaf discs were then freeze-dried and weighed to the nearest 0.1 mg. Triton X-100 (0.5 mL of 0.5% solution) was added to the spore suspensions, which were stirred gently to ensure the uniform distribution of spores. Aliquots of 5 mL were then filtered through a membrane filter (SMWP, 25 mm diameter, pore size 5 lm; Millipore, Bedford, MA, U.S.A.), and the spores on the filter were stained with 0.1% Trypan blue in 60% lactic acid. Spores were counted and identified under the microscope (•200), according to [START_REF] Gulis | An illustrated key to the common temperate species of aquatic hyphomycetes[END_REF]. Spore production was calculated as the number of spores released per g leaf AFDM per d. The Shannon diversity index (H') and the Shannon evenness index (E H¢ ) were computed from the cumulative spore production after 19, 35, 56 and 82 days of exposure for fungal communities associated with each of the four treatments.

Fungal biomass in leaf litter was quantified using ergosterol content as an estimator of mycelial biomass [START_REF] Gessner | Ergosterol-to-biomass conversion factors for aquatic hyphomycetes[END_REF]. The five frozen leaf discs were freeze-dried, weighed to the nearest 0.1 mg and heated at 80 °C for 30 min with alkaline methanol to extract the lipids. Extracts were purified using solid-phase extraction cartridges (Oasis HLB, 60 mg, 3 cc; Waters, Milford, MA, U.S.A.), then quantified by high-performance liquid chromatography. Ergosterol content was then converted to mycelium biomass (mg g )1 AFDM of litter), assuming that 5.5 mg of ergosterol represents 1 g of fungal dry matter [START_REF] Gessner | Ergosterol-to-biomass conversion factors for aquatic hyphomycetes[END_REF].

To describe oak litter quality to shredding invertebrates, two parameters were measured: leaf litter toughness and elemental composition. Leaf toughness is an important parameter for leaf litter consumption by invertebrates [START_REF] Arsuffi | Leaf processing capabilities of aquatic hyphomycetes: interspecific differences and influence on shredder feeding preferences[END_REF], particularly in low palatability species such as oak, and was estimated by measuring the force needed to penetrate leaf samples using a penetrometer similar to that described in the study by [START_REF] Grac | Methods to Study Litter Decomposition: A Practical Guide[END_REF]. The punch (diameter: 1.55 mm) was placed in the centre of an area bounded by the leaf veins. Water was loaded on a piston until the punch broke through the leaf. The mass (mg) of water necessary to break through the leaf was converted into penetration pressure (kPa) and then used as a measure of leaf toughness. For each treatment replicate, leaf toughness corresponded to the mean of 15 measurements on at least five distinct leaves. Finally, leaf litter elemental ratios were chosen as good estimators of detrital organic matter decomposability [START_REF] Enriquez | Patterns in decomposition rates among photosynthetic organisms: the importance of detritus C:N:P content[END_REF] and essential parameters affecting consumer life-history traits [START_REF] Sterner | Ecological Stoichiometry: The Biology of Elements From Molecules to the Biosphere[END_REF]. To estimate the leaf litter elemental quality for consumers, C, N and P contents were measured at each sampling date. Analyses were carried out on previously ground material. The percentages of C and N contained in leaf litter were determined using a CHN elemental analyzer (NA 1500 Series 2; Fisons, Manchester, U.K.). Total P content was determined after mineralisation by alkaline oxidation with sodium persulphate [START_REF] Danger | Effects of food web structure on periphyton stoichiometry in eutrophic lakes: a mesocosm study[END_REF]. All elemental ratios were expressed as molar ratios.

Invertebrate feeding rates

To investigate the effect of leaf litter burial in the hyporheic zone of streams on its palatability to invertebrates, we chose three distinct representative shredder taxa of Western European headwater streams. The crustacean Gammarus fossarum Koch is widespread and common in headwater streams, often playing a major role in leaf litter breakdown [START_REF] Felten | Quantification of diet variability in a stream amphipod: implications for ecosystem functioning[END_REF]. While present at the surface of the sediment, this species was never found in the hyporheic zone of the studied stream [START_REF] Cornut | Early stages of leaf decomposition are mediated by aquatic fungi in the hyporheic zone of woodland streams[END_REF]. Sericostoma personatum Kirby & Spence is the most common trichopteran present in the studied stream, and small individuals are able to access buried leaf litter [START_REF] Cornut | Early stages of leaf decomposition are mediated by aquatic fungi in the hyporheic zone of woodland streams[END_REF]. Finally, the plecopterans Leuctra spp. are among the most efficient taxa at penetrating the hyporheic zone thanks to their body morphology, and have access to buried organic matter [START_REF] Cornut | Early stages of leaf decomposition are mediated by aquatic fungi in the hyporheic zone of woodland streams[END_REF].

Leaf litter palatability to selected shredder taxa was determined through short-term non-choice feeding assays [START_REF] Elger | Determinants of macrophyte palatability to the pond snail Lymnaea stagnalis[END_REF] after 35, 56 and 82 days of leaf litter conditioning in the stream. Individuals of the three invertebrate taxa were acclimatised in the laboratory for at least 7 days at 10 °C before the experiments and supplied ad libitum with plant detritus from the stream. The experiments were carried out in plastic containers (125 mL), filled with 60 mL of filtered stream water (GF ⁄ C filters, Whatman, nominal cut-off 1.2 lm), at 10 °C. For G. fossarum and S. personatum, tests were performed individually, whereas for Leuctra spp., relatively small species compared with the two others, five individuals were used for each trial to limit the duration of the test and consequently respect the conditions necessary for non-choice palatability measurements [START_REF] Elger | Determinants of macrophyte palatability to the pond snail Lymnaea stagnalis[END_REF]. For each taxon, individuals were sorted out by size class (dry mass ± SD: 6.8 ± 0.7 mg for G. fossarum, 0.59 ± 0.07 mg for Leuctra spp., and 13.4 ± 2.3 mg for S. personatum). Three pairs of 10-mm leaf discs were cut from the same leaf, that is, one pair for each taxon. All leaf discs were weighted to the nearest 0.01 mg after being quickly dried on a clean absorbent paper. For each invertebrate taxon, one leaf disc was available as food on the bottom of the container and the second one (control) was enclosed in a small fine-mesh (250-lm) bag attached to the container's edge. The length of palatability test was adjusted to reach c. 50% of mass loss in at least one treatment, that is, 11 h for S. personatum, from 45 to 48 h for Leuctra spp. and from 68 to 72 h for G. fossarum. Then, unconsumed and control leaf discs as well as invertebrates were dried at 65 °C to constant mass and weighed to the nearest 0.01 mg. Dry mass (DM) of the leaf disc available as food for consumers was estimated from its initial fresh mass multiplied by the ratio of DM to fresh mass of the control leaf disc. Relative consumption rates were calculated as the DM consumed divided by the DM of consumers and by the time of the consumption experiment. Relative consumption rates were expressed as mg mg )1 consumer per day. Consumption rates were measured independently for each invertebrate taxon four times per treatment per replicate riffle (i.e. 16 measurements per treatment per date) and then averaged by riffle to avoid pseudoreplication (four independent data per treatment per date).

Individual consumer growth rates

To test for the effects of leaf litter conditioning treatments on consumer life-history traits, we carried out individual growth measurements on males of G. fossarum fed with leaf litter subject to these treatments. This crustacean species was preferred to the two other taxa, owing to its robustness for relatively longterm experiments. As for palatability measurements, G. fossarum were collected in the field and acclimatised in the laboratory for at least 7 days at 10 °C, then sorted by size and put into clear water without food 48 h before starting the experiments. We verified that organisms did not differ significantly between treatments and dates at the beginning of the experiment (15.6 ± 1.8 mg wet mass). To test for the effect of the duration of leaf litter conditioning on the different treatments, the experiment was carried out at two sampling dates, after 35 and 82 days of conditioning. At these sampling dates, 12-mm leaf discs were cut. To limit any alteration in leaf litter quality during the 3-week experiment, leaf discs were immediately frozen at )18 °C before their distribution to consumers. Males of G. fossarum were put individually in 125-mL containers filled with 60 mL of filtered stream water. Organisms were fed ad libitum with two leaf discs. Every second day, leaf discs were recovered and replaced by new leaf discs and water was changed and replaced by filtered aerated stream water. Experiments were carried out at 10 °C. All organisms were weighed at the beginning and at the end of the experiment to the nearest 0.01 mg after being quickly drained on clean absorbent paper. As for palatability tests, each measurement was conducted on sixteen samples, that is, four per riffle, which were averaged to obtain a mean value for each treatment and replicate riffle. One individual died on the first day of the experiment with 35-days litter and was immediately replaced. G. fossarum growth was calculated as the percentage of the difference between final and initial mass against initial mass.

Statistical analyses

Leaf litter decomposition rates (k) were calculated using the exponential decay model as follows: M t = M o AEe )kt , where M o represents the initial AFDM, M t the remain-ing AFDM at time t and t the time in d spent since the beginning of the experiment. Analysis of covariance (ANCOVA A N C O V A ) made on logarithmically transformed AFDM data was used to test for the effects of burial treatment on leaf litter decomposition. Differences between physicochemical conditions in hyporheic and benthic zones of the stream were tested using a two-way A N O V A A N O V A , with time and location as categorical predictors. For all measured parameters (leaf litter toughness, elemental quality, fungal biomass, aquatic hyphomycete sporulation rates, leaf litter consumption rate and G. fossarum growth rate), the effects of burial treatment, time and their potential interactions were examined using twoway ANOVAS N O V A S . Data were log-transformed to improve the homoscedasticity when necessary. Because of systematic differences in physicochemical conditions in one of the four replicate riffles, and to correct for this potential bias, this parameter was introduced in all analyses as a block effect. In fact, this parameter was only shown as significantly affecting the P content of buried leaf litter and was thus removed from the other analyses. For all analyses, multiple comparisons were made using Tukey's HSD test. STATISTICA (StatSoft Inc, 2001) was used for all statistical analyses cited above. The similarity between aquatic hyphomycete communities at each sampling date under the various treatments was measured with the Steinhaus index [START_REF] Legendre | Numerical Ecology[END_REF] using R software version 2.6.0 (R Development Core Team, 2007). For all analyses, a significance threshold of P = 0.05 was chosen.

Results

Physicochemical conditions in benthic and hyporheic zones

All physicochemical parameters measured throughout the experiment differed significantly between the hyporheic zone and the benthic zone of the river (Table 1). Oxygen was significantly lower in the hyporheic than in the benthic zone, showing a reduction by c. 40%. Conductivity and P content of interstitial water were systematically higher than those of surface water. Temperature was on average 0.4 °C higher in the hyporheic compartment. This result can be related to the fact that one of the four riffles showed higher temperature of interstitial water during the first 80 days of the experiment and less variation in temperature throughout the experiment than other riffles. This riffle was characterised by a positive VHG, indicating an upwelling-type functioning (discharge from the interstitial zone into surface water), whereas the three other riffles, which showed negative VHG throughout the experiment, were downwelling zones.

Leaf litter decomposition and conditioning

There was a marked variation in the decomposition of oak leaves as a function of burial treatment (Table 2). In all treatments, leaves lost up to 10% of their mass during the first 7 days of the experiment. Then, decomposition followed a classical exponential pattern (data not shown), which differed among burial treatments. Leaf litter decomposition was significantly faster when exposed in the benthic zone of the stream, intermediate in the HB treatment and the lowest in the H and BH treatments (Table 2).

Mycelial development of aquatic fungi, as measured by ergosterol content, was significantly affected by burial treatment (F 15,72 = 1.87, P = 0.041). Fungal biomass increased quickly to a first plateau during the first 20 days (Fig. 1), this plateau being independent of burial treatment. After 60 days, fungal biomass reached a second plateau, this one being significantly higher (by more than 30%) in B than in the three other treatments.

The pattern of spore production of leaf-associated aquatic hyphomycetes was quite similar between treatments, increasing throughout the experiment (Fig. 2). However, the sporulation rate in treatment B showed a sharp increase to reach a peak of 195 spores mg )1 AFDM d )1 at day 82, whereas maximal values of sporulation rate were lower in the BH, H and HB treatments. As a consequence, sporulation rates in the B treatment were higher than those of the three other treatments (F 3,56 = 5.73, P = 0.002).

A total of 30 sporulating species of aquatic hyphomycete were identified from decomposing leaves with a quite similar number (19-24) found in the four exposure treatments (Table 3). Considering the heterogeneity of fungal assemblages, no single species was shown as significantly differing between treatments. However, similarity analyses carried out on communities showed that aquatic hyphomycete communities were relatively similar between B and BH treatments (Steinhaus similarity index = 0.654) at day 19, the time of burial or removal of leaf material from sediment. In contrast, these two treatments differed markedly from those subject to an initial exposition to the hyporheic zone. Steinhaus similarity index at this date ranged from 0.022 to 0.080 between the four treatments. The similarity between B and HB treatments increased throughout the experiment to reach its maximum with a Steinhaus similarity index of 0.868 at day 82. At this date, the similarity of the H treatment with the HB and B ones had also increased, but was only 0.438 and 0.452, respectively. The Shannon diversity indices observed for H and HB were higher than those for the two other treatments, whereas evenness values across the four treatments were quite similar (Table 3).

Leaf litter quality to consumers

Oak leaf litter toughness (Fig. 3) decreased continuously during the experiment (F 3,48 = 44.4, P < 10 )4 ), but was on average 20% lower in the benthic-exposed leaves than in the three other treatments (F 3,48 = 7.6, P < 10 )3 ).

Both C ⁄ P and C ⁄ N ratios (Fig. 4) of leaf litter exposed in the stream decreased significantly throughout the experiment (F 5,69 = 19.4, P < 10 )4 and F 5,72 = 9.76, P < 10 )4 , respectively). In contrast, leaf litter N ⁄ P ratio was constant during the experiment (time: F 5,72 = 0.82, P = 0.535; interaction time x treatment: F 15,72 = 0.15, P = 0.999). Leaf litter C ⁄ N and N ⁄ P ratios were not significantly affected by the exposure treatment (F 3,72 = 0.52, P = 0.663 and F 3,72 = 0.42, Numbers in parentheses represent minimal and maximal values recorded. P-values indicate the significance of differences between average determinations in the two stream compartments. Legends of treatments are the same as in Table 2. Vertical bars correspond to ±1 SE. P = 0.737, respectively), whereas leaf litter C ⁄ P ratio was significantly lower in B than in the three other treatments (F 3,69 = 2.76, P = 0.048). C ⁄ N and C ⁄ P ratios were negatively correlated with the mycelial content of the leaf (r 2 = 0.34, n = 96, P < 10 )4 and r 2 = 0.49, n = 96, P < 10 )4 , respectively). In addition, leaf litter toughness was also negatively correlated with the mycelial content of the leaf (r 2 = 0.54, n = 80, P < 10 )4 ).

Feeding rate of invertebrates

Leaf litter palatability, as measured by short-term consumption rates of a leaf disc, differed as a function of the duration of the exposure and the type of consumer tested (Fig. 5).

Leaf litter consumption rate by G. fossarum significantly increased with the length of conditioning in the stream (F 2,36 = 17.7, P < 10 )4 ). Consumption rates of leaf litter by S. personatum were slightly higher after 56 days of exposure in the stream than for the two other conditioning durations tested (F 2,36 = 5.06, P = 0.011). In contrast, consumption rates of leaf litter by the plecopteran Leuctra were unaffected by the duration of leaf litter conditioning (F 2,36 = 0.78, P = 0.465).

For the three invertebrates tested, leaf litter exposed in the benthic zone of the stream was on average consumed more than leaf litter exposed in the hyporheic zone throughout the experiment (F 3,36 = 3.69, P = 0.021; F 3,36 = 3.20, P = 0.035; and F 3,36 = 3.44, P = 0.027 for G. fossarum, S. personatum and Leuctra, respectively).

Leaf litter palatability to S. personatum was significantly related to leaf litter C ⁄ P ratio (r 2 = 0.14, n = 48, P = 0.009). Leaf litter palatability to Leuctra was slightly negatively related to leaf litter toughness (r 2 = 0.09, n = 48, P = 0.041) Legends of treatments are the same as in Table 2.

and C ⁄ P ratio (r 2 = 0.09, n = 48, P = 0.037). Finally, leaf litter palatability to G. fossarum was more strongly, negatively related to leaf litter toughness (r 2 = 0.31, n = 48, P < 10 )4 ) and C ⁄ P ratio (r 2 = 0.13, n = 48, P = 0.011) and positively related to the mycelial content (r 2 = 0.31, n = 48, P < 10 )4 ).

Effect of leaf litter burial on consumer growth rates

Individual growth rates of G. fossarum showed a significant effect of leaf litter exposure treatment (F 1,27 = 3.53, P = 0.028, Fig. 6). Growth rates of G. fossarum did not differ significantly when fed with leaf litter conditioned for 35 and 82 days in the stream (F 1,24 = 2.37, P = 0.135). However, there were significantly higher growth rates when fed with leaves from B than from the H treatment. G. fossarum growth rate was neither correlated with leaf litter toughness nor correlated with palatability. However, it was negatively related to leaf litter C ⁄ P ratio (r 2 = 0.13, n = 32, P = 0.046).

Discussion

Leaf litter decomposition and fungal communities

Our results indicate that leaf litter decomposition by microorganisms is significantly reduced in the hyporheic zone compared with the benthic zone of headwater streams. This result is in contradiction with the only other study comparing litter decomposition in fine-mesh bags between hyporheic and benthic zones of streams Elemental ratios are molar ratios. Legends of treatments are the same as in Table 2. Vertical bars correspond to ±1 SE. [START_REF] Rounick | Leaf processing in 2 contrasting beech forest streams -effects of physical and biotic factors on litter breakdown[END_REF], where decomposition patterns were found not to differ. Interestingly, we found no differences in mycelial biomass or in decomposition rates between leaves that were subject to a burial stage whatever its duration or timing (i.e. H, BH or HB), with both variables being c. 20% lower than in the benthic zone at the end of the exposition period. The spore production, being two to three times lower than in the permanently benthic condition, was more impacted. Consequently, burial of leaf litter in the hyporheic zone of the stream, whatever its duration, significantly altered the microbial colonisation and delayed the decomposition of detrital organic matter.

In line with the results of [START_REF] Cornut | Early stages of leaf decomposition are mediated by aquatic fungi in the hyporheic zone of woodland streams[END_REF] for alder leaves, the structure of fungal assemblages associated with oak leaves was affected by burial in sediment. While benthic and benthic-hyporheic communities were initially quite similar, they strongly diverged after several weeks of exposure in the stream, in contrast with benthic and hyporheic-benthic fungal communities that converged. This, together with the patterns related above, suggests that (i) the fungal inoculum is more abundant or efficient when originating from the benthic environment than from the hyporheic and (ii) the latter environment is less favourable to fungal development. In addition, aquatic hyphomycete communities developing in hyporheic and benthic zones differed, probably reflecting better adaptation of individual species to the conditions prevailing in either environment. Whether some species were sensitive to the reduction in oxygen concentration (Medeiros, Gammarus consumption rates Pascoal & Grac ¸a, 2009), the higher P availability in the hyporheic zone or other parameters remains unknown.

Overall the positive effect of inorganic P in water was, nevertheless, small as judged by the C ⁄ P ratios in hyporheic litter, which was higher than in benthic litter.

The qualitative and quantitative differences in fungal assemblages and development were more pronounced on alder leaves [START_REF] Cornut | Early stages of leaf decomposition are mediated by aquatic fungi in the hyporheic zone of woodland streams[END_REF] than on oak leaves (this study), with both studies being carried out in the same stream with a gap of 1 year. These differences observed between two contrasting types of leaf litter probably result from differences in substratum recalcitrance, which in the case of oak led to a delayed and limited extent of the development of fungal communities [START_REF] Bengtsson | Habitat selection in two species of aquatic hyphomycetes[END_REF][START_REF] Gessner | Importance of stream microfungi in controlling breakdown rates of leaf litter[END_REF][START_REF] Chauvet | The impact of eucalypt on the leaf-associated aquatic hyphomycetes in Spanish streams[END_REF][START_REF] Gulis | Are there any substrate preferences in aquatic hyphomycetes[END_REF].

Leaf litter consumption by invertebrates

In this study, we showed that leaf litter palatability to invertebrate consumers was higher when leaf litter was incubated in the benthic zone than in the hyporheic zone of the stream. These results are in accordance with those reported by [START_REF] Herbst | Effects of burial on food value and consumption of leaf detritus by aquatic invertebrates in a lowland forest stream[END_REF] of reduced palatability of ash and poplar leaves to invertebrate consumers. In our study, leaf litter palatability greatly differed between the three invertebrate consumer taxa tested, with consumption rates increasing with time only for G. fossarum. In addition, while palatability was related to leaf litter toughness for two of the three invertebrates, the relationship was far stronger for G. fossarum. These results may be related to differences in feeding behaviour and mouth parts anatomy of these invertebrate taxa. Leaf toughness can influence food selection by building a physical barrier for invertebrate feeding, harder leaves being more difficult to tear than soft ones [START_REF] Pennings | Feeding preferences of a generalist salt marsh crab: relative importance of multiple plant traits[END_REF][START_REF] Motomori | Influence of leaf litter quality on the colonisation and consumption of stream invertebrate shredders[END_REF]. This is especially relevant for G. fossarum, which eats the whole leaf matter, consisting of both fungi and leaf matrix, and is limited by its feeding apparatus when leaf remains too hard [START_REF] Grac | Importance of fungi in the diet of Gammarus pulex (L.) and Asellus aquaticus (L.): II Effects on growth, reproduction and physiology[END_REF]. This species appears to be a particularly interesting biological model because of its dependence on microbial conditioning of leaf detritus. In contrast, the small plecopteran Leuctra only feeds by scraping the surface of the leaf discs. Because toughness measurements integrate the whole leaf thickness, this parameter is certainly not pertinent for this type of consumer. The independence of the consumption by the trichopteran S. personatum from leaf toughness is probably related to its ability to eat poorly conditioned and hard materials.

Only a small part of the observed patterns of leaf litter palatability to consumers can be explained from the measured biological and physicochemical parameters. Several studies have showed that, more than total fungal biomass in leaf litter, the fungal species present can shape the response of invertebrate consumers (e.g. [START_REF] Butler | Aquatic hyphomycetes on oak leaves: comparison on growth, degradation and palatability[END_REF]. Given that shredding invertebrates have feeding preferences for litter colonised by certain fungal species [START_REF] Ba ¨rlocher | Hyphomycetes as intermediaries of energy flow in streams[END_REF][START_REF] Arsuffi | Leaf processing capabilities of aquatic hyphomycetes: interspecific differences and influence on shredder feeding preferences[END_REF][START_REF] Arsuffi | Selective feeding by caddisfly (Trichoptera) detritivores on leaves with fungal colonized patches[END_REF], 1989;[START_REF] Butler | Aquatic hyphomycetes on oak leaves: comparison on growth, degradation and palatability[END_REF], differences can be anticipated in consumption and growth rate between invertebrates fed on litter colonised by different assemblages [START_REF] Arsuffi | Leaf processing capabilities of aquatic hyphomycetes: interspecific differences and influence on shredder feeding preferences[END_REF][START_REF] Arsuffi | Selective feeding by caddisfly (Trichoptera) detritivores on leaves with fungal colonized patches[END_REF]. In our study, fungal assemblage but not total species richness was altered by leaf exposure in the hyporheic zone of the stream. Recently, Chung & Suberkropp (2009) demonstrated that ecological efficiencies (i.e. larval survivorship, relative consumption rate, gross growth efficiency and instantaneous growth rate) of limnephilid larvae were more affected by fungal species identity than diversity. Similarly, we can hypothesise burial to indirectly affect leaf litter palatability through the selection of fungal species that are more or less palatable. Consumption rates of leaf litter by the three selected invertebrate taxa of our study could thus, at least partly, be driven by alterations in the fungal community. Experimental approaches using litter inoculated with controlled fungal assemblages are, however, required to confirm this hypothesis.

Overall, our results clearly show that burial of leaf litter can strongly decrease its consumption by invertebrate consumers and thus lower nutrients and energy transfer to higher trophic levels. However, the timing and sequences of leaf litter burial, for example a short colonisation period occurring in the benthic zone before burial, could alleviate these effects. In addition, the impact of leaf litter burial on its consumption by invertebrates certainly depends on the shredder identity and its ability to access buried organic matter. [START_REF] Cornut | Early stages of leaf decomposition are mediated by aquatic fungi in the hyporheic zone of woodland streams[END_REF] showed that Leuctra spp. and small individuals of S. personatum but not G. fossarum were able to colonise leaf litter buried in the hyporheic zone of this stream. Reduced litter palatability should thus directly impact leaf litter breakdown by species able to access buried leaf litter, while consequences of the reduction in leaf litter palatability to shredders unable to penetrate sediment should only depend on sediment movements that make this litter accessible.

Consumer growth rates

Exposure in the hyporheic zone not only negatively impacted leaf litter palatability, but also impacted growth rates of G. fossarum. Maximal growth rates were observed when organisms were fed with leaf litter exposed at the surface of sediment throughout the experiment. G. fossarum growth rate was negatively correlated with leaf litter C ⁄ P ratio but was independent of leaf litter toughness and palatability. These results are in accordance with the 'Growth Rate Hypothesis', the resource content in P being often limiting consumer growth [START_REF] Elser | Growth rate-stoichiometry couplings in diverse biota[END_REF]. To our knowledge, it is the first time that such a relationship has been shown for detritivorous invertebrates. Nevertheless, the relationship is weak, and several other factors (e.g. secondary compounds) may interact with P content to influence the invertebrate growth. The role of resource P content in regulating key life-history traits of headwater stream detritivores, food web structure and related functional processes remains to be explored in further studies.

In conclusion, our study shows that the exposure of leaf litter in the hyporheic zone of a headwater stream, even for a short period, alters the microbial development and leaf litter conditioning. These modifications can in turn negatively impact leaf litter palatability to consumers as well as a major detritivorous consumer life-history trait, i.e. growth rate. The results highlight the key role of aquatic hyphomycetes in the conditioning of leaf litter in the hyporheic zone, which is at least as influential as in surface habitats. The constraining conditions of the hyporheic zone and the disturbances related to the burial history have markedly impacted fungal development not only by delaying the accrual of mycelial biomass on leaf litter, but also by modifying the structure and composition of the species assemblages. Even if the mechanisms underlying the feeding preferences of invertebrate consumers remain unclear, fungal species identity may be crucial in controlling leaf consumption by shredders. The low decomposition rates observed, as well as the delay in quality improvement compared with benthic-exposed leaves, also imply that the hyporheic zone of woodland streams acts as an important compartment for organic matter storage and food provision to detritivorous organisms after sediment movements, particularly when new detrital inputs are scarce. This temporary reservoir of resources may affect the overall stream metabolism and should thus be taken into account in further studies considering the functioning, the conservation or the restoration of headwater stream ecosystems.

Fig. 1 Fig. 2

 12 Fig.1Changes in mycelial biomass (derived from ergosterol contents) in oak litter as a function of exposure treatment in the benthic and hyporheic zones of the stream. Legends of treatments are the same as in Table2. Vertical bars correspond to ±1 SE.

Fig. 3 Fig. 4

 34 Fig.3Leaf litter toughness as a function of exposure treatment. Legends of treatments are the same as in Table2. Vertical bars correspond to ±1 SE.

(Fig. 5

 5 Fig. 5 Leaf litter palatability to three taxa of benthic invertebrate consumers: Gammarus fossarum (Crustacea), Sericostoma personatum (Trichoptera) and Leuctra spp. (Plecoptera), as a function of leaf litter exposure treatment. Leaf litter palatability measurements were taken on leaf litter exposed for 35, 56 and 82 days in the different treatment conditions. Legends of treatments are the same as in Table 2. Vertical bars correspond to ±1 SE.

Table 1

 1 Physical and chemical characteristics of the benthic and hyporheic zones of the stream. Values are means ± SE of data collected during the experiment (from January to May 2009)

	Variable	Benthic	Hyporheic	P
	O 2 (% saturation)	104.9 ± 0.2 (101-107)	61.4 ± 17.7 (39-95)	<10 )4
	pH	6.2 ± 0.1 (5.6-6.6)	5.9 ± 0.1 (5.0-6.6)	<10 )4
	Conductivity (lS cm )1 )	27.4 ± 0.9 (14-35)	35.3 ± 2.5 (22-46)	<10 )4
	Temperature (°C)	6.2 ± 0.2 (4.0-10.4)	6.6 ± 0.5 (4.1-10.4)	0.011
	NO 3 -N (mg L )1 )	0.91 ± 0.02 (0.71-1.09)	0.83 ± 0.09 (0.52-1.01)	0.005
	SRP (lg L )1 )	1.55 ± 0.23 (0.45-5.07)	9.61 ± 1.89 (3.98-19.62)	<10 )4

Table 2

 2 Daily exponential decay rates (k) of oak leaves as a function of exposure treatment: B, leaf litter exposed at the surface of the sediment throughout the experiment; BH, leaf litter exposed for 3 weeks at the surface of the sediment before being buried in the hyporheic zone; HB, leaf litter exposed for 3 weeks in the hyporheic zone before being exposed at the surface of the sediment; H, leaf litter exposed in the hyporheic zone throughout the experiment

	Treatment	k (d )1 )	r 2	T 50 (d)
	Benthic (B)	0.0036 a	0.95	191
	Benthic-Hyporheic (BH)	0.0029 b	0.88	240
	Hyporheic-Benthic (HB)	0.0031 ab	0.91	221
	Hyporheic (H)	0.0029 b	0.87	242
	Different letters represent significantly different treatments. Regres-
	sion coefficients and time to reach 50% of leaf mass loss are also
	indicated.

Table 3

 3 Relative abundance (%) of the leaf-associated aquatic hyphomycete species and diversity indices determined from the cumulative spore production after 19, 35, 56 and 82 days of exposure for the four exposure treatments (four replicate leaf bags combined)

	Species

Table 2

 2 Effects of leaf litter burial on Gammarus fossarum growth rates during 3-week experiments. Values are expressed as percentages of initial mass. Growth rates were determined for animals fed with 35-and 82-day-old leaf material. Legends of treatments are the same as in Table2. Vertical bars correspond to ±1 SE.

	. Vertical

Acknowledgments

We are grateful to Fre ´de ´ric Julien, Didier Lambrigot and Sylvain Lamothe for their technical help. This manuscript also benefited from constructive comments by Felix Ba ¨rlocher, Manuel A.S. Grac ¸a, Franc ¸ois Gue ´rold, Florian Mermillod-Blondin and two anonymous reviewers. This study was funded through the InBioProcess project of the French ANR Biodiversity programme (ANR-06-BDIV-007).


Oscar Sánchez

Christophe Jégo
email: christophe.jego@ims-bordeaux.fr.

Member IEEE Michel Jézéquel
email: michel.jezequel@telecom-bretagne.eu.

Analysis of the Convergence Process by EXIT Charts for Parallel Implementations of Turbo Decoders

Iterative process is a general principle in decoding powerful FEC codes such as turbo codes. However, the mutual information exchange during the iterative process is not easy to analyze and to describe. A useful technique to help the designer is the EXtrinsic Information Transfer (EXIT) chart. Unfortunately, this method cannot be directly applied to the decoding convergence analysis if parallel processing has to be exploited for the design of turbo decoders. In this letter, an extension of the EXIT charts method is proposed in order to take into account the constraints introduced by parallel implementations. The corresponding analysis associated with Monte-Carlo simulations gives additional understanding of the convergence process for the design of parallel architectures dedicated to turbo decoding.

I. INTRODUCTION

T URBO coding [1] is a well-known channel-coding tech- nique widely used in digital communications because of its error correcting capabilities close to the Shannon limit. It is especially attractive for wireless communications where several standards, such as UMTS, CDMA2000 or 3GPP-LTE, have adopted it. However, the design of high throughput Turbo Decoders (TDs) is a major challenge in today's systems. Indeed, the next generations of mobile communication systems will require data rates of 1 Gb/s and beyond. To respond to this challenge, designers have to exploit the maximum feasible amount of parallelism in TDs. The decoding of turbo codes is carried out through an iterative process where two Soft-Input Soft-Output (SISO) decoders, operating in natural and interleaved domain, exchange extrinsic information. SISO decoding algorithm is usually known as the Maximum A Posteriori (MAP), Forward-Backward or Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. MAP-based algorithms such as Log-MAP and Max-Log-MAP [START_REF] Robertson | A comparison of optimal and suboptimal map decoding algorithms operating in the log domain[END_REF] are the most common decoding algorithms for a hardware implementation. Unfortunately, these algorithms implement recursive operations making them difficult to parallelize.

Various parallelism techniques have been proposed in order to design high throughput TDs. In [START_REF] Muller | Exploring parallel processing levels for convolutional turbo decoding[END_REF], a multi-level classification of parallel turbo decoding techniques with three hierarchical levels has been proposed: TD level parallelism, SISO decoder level parallelism and metric computation level parallelism. The first parallelism level corresponds to the duplication of the turbo decoder architecture. Since this level is not efficient in terms of hardware resources and frame decoding latency, it is not considered in this work. SISO decoder level parallelism consists in the use of several SISO decoders that work simultaneously. Two well-known techniques have been proposed. The first one is referred to as subblock parallelism, and the second one as shuffled parallelism. In sub-block parallelism each received frame is divided into several sub-blocks. Then, each sub-block can be decoded in parallel. The basic idea of shuffled decoding is to decode both constituent convolutional codes simultaneously, exchanging extrinsic values as soon as possible [START_REF] Zhang | Shuffled iterative decoding[END_REF]. The metric computation level parallelism exploits on one hand the parallelism of the trellis structure and, on the other hand, the parallelism of metric computation [START_REF] Masera | Vlsi architectures for turbo codes[END_REF].

In all previous works, the BER performance degradation introduced by parallel processing is not explicitly considered and analyzed. Generally, to overcome the BER performance lost additional iterations are executed, with a corresponding negative impact on the TD throughput. A behavior analysis has to be performed to estimate the convergence of these techniques that increase the parallelism level. Moreover, new schedules have to be explored based on Monte-Carlo simulations associated to EXIT charts for designing decoding architectures suitable with high throughput. In this letter, we study the relation between different parallelism techniques and the additional TD iterations executed to prevent BER performance lost. An extension of the current EXIT chart technique is particularly proposed to enable the convergence analysis of the parallel decoding process.

This letter is organized as follows. Section II presents parallel techniques commonly used to increase the TD throughput. Section III introduce an extension of the EXIT chart method to analyze parallel TDs by adapting the usual method. In section IV parallel TD schemes are analyzed considering their transfer characteristics. A modified schedule for the computations inside the SISO decoders is also proposed.

II. PARALLEL TURBO DECODING APPROACHES

We recall that metric computation and SISO decoder are the two parallelism levels considered due to their efficiency.

A. Metric computation parallelism level

Some parallelism can be achieved depending on the way the computations are executed by each SISO decoder. Note that we refer to schedule as the organization of the MAP-based algorithm computations. Fig. 1 depicts four different schedules for the decoding process over a sub-block of N information symbols. From the expression of the Forward-Backward algorithm, several schedules can be devised. A common schedule that produces soft output values in natural order is called Backward-Forward (B-F). This schedule is considered as reference in the remainder of this letter (Fig. 1(a)). Initially, β state metrics are computed recursively starting from the end until the beginning of a sub-block. β values are memorized. When all β values of the sub-block of size N are computed, α state metrics computation can start. In parallel, thanks to the β values previously computed, soft output values L a,k are calculated in natural order. In the Backward-Forward schedule, the decoding process duration is equal to twice the length N of a sub-block. This duration is halved by using the Butterfly schedule (Fig. 1(b)), at the cost of doubling the hardware resources to compute α, β and L a,k . Schedules Butterfly-Forward and Butterfly-Replica in Fig. 1(c) and 1(d) respectively, have the same decoding duration as the Butterfly schedule. However, they generate a-posteriori values continuously. To this end, some state metrics values have to be stored at the end of each half iteration. Both schedules were defined to improve the convergence of shuffled TDs.

Let the 3-tuple Φ ξ Q,S = {Q, S, ξ} denotes the parallelism level of a TD architecture with Q ≥ 1 the number of subblocks in the natural and interleaved domain, S the shuffled (Sh) or not shuffled (NoSh) parallelism, and ξ the decoding schedule -Backward-Forward (B-F), Butterfly (B), Butterfly-Forward (B-FW) or Butterfly-Replica (B-R) -. For convenience, we refer to this notation in the rest of the paper.

B. SISO decoder parallelism level

In order to exploit decoder parallelism, sub-blocks processing can be applied. The sub-blocks are processed in parallel in each domain and serially between the two domains, or in a full parallel manner. Since the computation of the state metrics α and β in the MAP-based algorithm are obtained by a recursive

SISO N 1 SISO N 2 SISO N Q Ie Ia Ψ(Φ, i) SISO I 1 SISO I 2 SISO I Q Fig. 2.
Architecture based on shuffled and sub-block parallelisms.

process, the sub-blocks are not independent. It means that the sub-block processing imposes a major constraint: the subblock initialization of state metrics α and β. A survey of subblock initialization can be found in [START_REF] Muller | Exploring parallel processing levels for convolutional turbo decoding[END_REF]. The initialization could be achieved by applying three different methods: initialization by acquisition, initialization by message passing and initialization by combining the two previous methods. We have chosen the second method that requires minimal additional hardware resources and has a minor impact on BER performance. Intuitively, in the shuffled decoding approach each SISO component has faster access to update a-priori values. It would enable a faster convergence, i.e. fewer iterations are necessary to achieve the same BER performance with respect to nonshuffled (serial) decoding approach. Indeed, extrinsic values are generated for both domains during each half iteration when shuffled parallelism is applied, while in the non-shuffled approach during a half iteration the extrinsic information of only one domain is generated. Moreover, sub-block and shuffled parallelism techniques can be combined. Thus, several SISO decoders work simultaneously on different sub-blocks in the natural and interleaved domain. This approach is shown in Fig. 2, where SISO N p and SISO I p for 0 < p ≤ Q are the decoders in the natural and interleaved domains respectively. An extrinsic memory is necessary to transfer extrinsic values between the decoders of the two domains. Two permutation networks are also necessary in order to provide interleaver and de-interleaver functions.

III. EXIT CHART METHOD EXTENSION

The EXtrinsic Information Transfer (EXIT) chart [START_REF] Brink | Convergence behavior of iteratively decoded parallel concatenated codes[END_REF] is a useful kind of diagram proposed to analyze the convergence process of iterative decoding systems. Let us consider a TD architecture Φ ξ 1,NoSh with no parallelism at the SISO decoder level. The transfer function that defines the relation between the mutual a-priori information at the input (I a ) and the mutual information at the output (I e ) of the sole SISO decoder in the architecture is given by ( 1) where E b /N 0 is the Signal to Noise Ratio (SNR).

I e = T (I a , E b /N 0 ) (1)
For a shuffled TD Φ ξm 1,Sh with a schedule ξ m ∈ {B-F, B} the transfer function in (1) holds as well. In [START_REF] Zhang | Iterative decoding with replicas[END_REF] a method to generate EXIT charts of shuffled TDs was introduced. Three Gaussian random noise generators are used: one for the channel and two others to generate the a-priori information. However, if a sub-block parallelism is applied in shuffled or not shuffled schemes, (1) is not valid anymore. Similarly, this equation cannot be applied to schedules B-FW and B-R with a shuffled parallelism. For these configurations, some values have to be kept during each half iteration in order to execute the next half iteration. It means that the transfer function has to take into account the dependency on additional parameters. Moreover, the EXIT chart method assumes that the extrinsic values have a Gaussian probability density function that has to satisfy the consistency condition. In this study, mean values of the EXIT band charts are considered to respect this constraint, as explained in [START_REF] Lee | Lower bound on ber of finite-length turbo codes based on exit characteristics[END_REF].

Let Ψ(Φ, i) denote the state of a TD with a parallelism level Φ, at the beginning of the half iteration i. For a subblock parallelism, Ψ(Φ, i) represents the initial state metric values α and β in the limits of the sub-blocks (dots • in Fig. 1). If schedules B-FW or B-R are considered, Ψ(Φ, i) also symbolizes α and β values inside the sub-blocks at the beginning of the decoding process of each half iteration (height of the shaded area at time t = 0 in Fig. 1(c) and 1(d)). Thus, the expression of the transfer function becomes:

I e = T (I a , E b /N 0 , Ψ(Φ, i)) (2)
For each value of E b /N 0 , we obtain a set of transfer curves that depends on the half iteration i. Fig. 3(a) shows the extrinsic information transfer characteristics for several iterations of the LTE TD with parallelism Φ B 128,NoSh at E b /N 0 = 1dB. Please note that the frame size is set to L = 6144 with a rate-1/2 code for all our experimentations. During the first iteration, the mutual information at the output is never equal to one, not even when the mutual information at the input is maximal. Iteration after iteration, the transfer characteristics improve so that the TD converges. When few iterations are performed the metrics in the limits of the sub-blocks after each iteration (Ψ(Φ B 128,NoSh , i)) are not good enough. Hence, even with a perfect knowledge of the information to decode (I a = 1) at the input of the SISOs, the decision taken is wrong (I e < 1). As more iterations are executed, better values for Ψ(Φ B 128,NoSh , i) are obtained letting the TD to converge. The decoding trajectory for the TD Φ B 128,NoSh is given in Fig. 3(b). For convenience the TD characteristics are only shown for some iterations. Each transfer curve is plotted up to its first intersection. The decoding trajectory is thus plotted by "jumping" between the different transfer curves as the iterations are carried out. Thus, the EXIT chart or decoding trajectory of any parallel TD Φ can be plotted. In this way, convergence of any parallelism scheme can be analyzed.

IV. TURBO DECODING CONVERGENCE ANALYSIS

Let us consider the architecture Φ r = Φ B 1,NoSh . The BER performance of this architecture after I(Φ r ) = 8 iterations is taken as reference for an unconstrained turbo decoding This performance is smaller than 0.1dB compared to that achieved by an ideal turbo-decoding algorithm and is compliant with the LTE standard. Thus, we desire that any parallel TD Φ have similar BER performance after I(Φ) iterations (no BER performance lost introduced by the TD parallelism). Convergence of the TDs Φ r , Φ B 32,NoSh , Φ B 128,NoSh and Φ B 512,NoSh , at SN R = [0.75dB, 1dB], are shown in Fig. 4. For SN R = 1dB, the number of iterations required for no BER performance degradation are I(Φ B 32,NoSh ) = 9, I(Φ B 128,NoSh ) = 11, I(Φ B 512,NoSh ) = 20, respectively. Since the duration of an iteration is reduced when more sub-blocks are used, it is possible to increase the TD throughput. Convergence of shuffled TDs Φ ξn 1,Sh with schedule ξ n ∈ {B, B-FW, B-R} is shown in Fig. 5. B-R schedule reduces significantly the number of iterations (almost to the half with respect to Φ r ). B and B-FW schedules have similar behaviors. However, the latter needs about one additional half iteration. For low SNR values both schedules behave almost identically.

EXIT charts of the different parallel TDs for whom convergence has been shown are presented in Fig. 6. The EXIT chart at SN R = 0.75dB of the architecture Φ r is depicted in Fig. 6(a). For this SNR value, the diagram starts just opening. It corresponds to the beginning of the "waterfall" region. The decoding trajectory of the TD Φ B 512,NoSh for some iterations is plotted as well. The need of additional iterations can be noted. of Φ B 32,NoSh is very close to the one that would follow Φ r . For thirteen iterations, the BER performance of Φ B 512,NoSh is worse than that of Φ B 32,NoSh with six iterations, which is also worse than that of Φ B 128,NoSh with eight iterations. Coherent results between Fig. 4 and Fig. 6(b) confirm the correctness of the decoding trajectories that have been obtained in Eq. ( 2). 1,Sh and Φ B-R 1,Sh behave similarly after the first half iteration, the decoding trajectory of the B-R schedule moves forward faster. Φ B-FW 1,Sh presents the worst characteristics to reduce the number of iterations. This occurs mainly due to the poor behavior after the first half iteration. Since during this half iteration β values of the first half of the sub-block are unknown (Fig. 1(c)), the a-posteriori values generated during the decoding of this part of the sub-block are not appropriate. After the first half iteration, all values α and β of the sub-block are properly calculated, and the decoding trajectory of the schedule B-FW tries to approach that of the EXIT chart of Φ B 1,Sh . However, the decoding trajectory cannot reach that of the Butterfly schedule and keeps at about one half iteration lower. This behavior does not appear for Φ B-R 1,Sh . Indeed for the schedule B-R, the a-posteriori values are computed with appropriate α and β values computed at each half iteration.

Since for shuffled parallelism the decoding is wider, shuffled TDs reach the region of waterfall at lower SNR values with respect to non-shuffled TDs. Fig. 6(d) illustrates how the decoding trajectory with schedule B-R can easily converge where the EXIT chart of Φ r becomes tight. Even more, for Φ B 1,Sh the EXIT chart is slightly wider than the EXIT chart of Φ r . It can be seen however that the decoding trajectory of Φ B-R 1,Sh narrows for high mutual input information.

When schedule B-R is used, at the beginning of each half iteration α and β values inside the sub-block (height of the shaded area in Fig. 1(d) at t = 0) correspond to the initial state of the TD. If those values are not good enough, they might prompt decoding errors even though the mutual information at the input of the SISO decoder is high. This behavior is similar to the one observed in Fig. 3(a), where not so good α and β values in the sub-block limits lead to errors in the early iterations for high input mutual information. No similar result is observed for Φ B 1,Sh since no initial values are kept from iteration to iteration. By taking into account this result, a new schedule can be proposed. It consists in employing B-R schedule during the early iterations, and then switching to Butterfly schedule. The decoding trajectory obtained for this new schedule (B-R&B) is presented in Fig. 6(d) where after 5 iterations the schedule is switched from B-R to B. Indeed, during the first 5 iterations the decoding trajectories of Φ B-R 1,Sh and Φ B-R&B 1,Sh are similar. Thus, fast convergence can be achieved, and since the hardware resources are the same for both schedules, no additional hardware complexity is required.

V. CONCLUSION Parallel turbo decoding techniques have been analyzed by observing the mutual information transfer characteristics of SISO decoders. Since the usual approach to plot EXIT charts cannot be directly applied, a key modification to this kind of diagrams has been proposed. In this way, EXIT charts become a useful method to understand the convergence of all parallel TDs. Moreover, a new schedule has been proposed for the shuffled TDs. Advantages of shuffled parallelism in order to reduce the number of iterations and to reach the waterfall region earlier have been observed. An integrated turbo decoder dedicated to LTE turbo codes has now been designed based on the current analysis for a 1 Gb/s experimental setup.

Fig. 1 .

 1 Fig. 1. Schedules for the MAP based algorithms: classical schedules ((a) Backward-Forward, (b) Butterfly) and schedules for shuffled turbo decoding ((c) Butterfly-Forward, (d) Butterfly-Replica).

Fig. 3 .

 3 Fig. 3. a) EXIT chart for a SISO decoder. b) decoding trajectory. (Parallelism Φ B 128,NoSh , E b /N 0 = 1dB, L = 6144 bits).

Fig. 4 .

 4 Fig. 4. Convergence of TDs with sub-block parallelism (L = 6144 bits).

Fig. 6 (Fig. 5 .

 65 Fig. 5. Convergence of shuffled TDs (L = 6144 bits).

Fig. 6 .

 6 Fig. 6. a) Decoding trajectory for Φ B 512,NoSh at 0.75dB. b) Decoding trajectories for 32, 128 and 512 sub-blocks no shuffled TDs. c) Decoding trajectories for shuffled TDs at 1dB. d) Decoding trajectories for schedules B-R, B and a combination of both at 0.75dB. Shuffled TDs EXIT charts for SN R = 1dB are presented in Fig. 6(c). EXIT chart of Φ B 1,Sh is wider than the EXIT chart of Φ r . For the B-R schedule the decoding trajectory exceeds that of the Butterfly schedule in shuffled mode (Φ B 1,Sh ). Even if Φ B1,Sh and Φ B-R 1,Sh behave similarly after the first half iteration, the decoding trajectory of the B-R schedule moves forward faster. Φ B-FW 1,Sh presents the worst characteristics to reduce the number of iterations. This occurs mainly due to the poor behavior after the first half iteration. Since during this half iteration β values of the first half of the sub-block are unknown (Fig.1(c)), the a-posteriori values generated during the decoding of this part of the sub-block are not appropriate. After the first half iteration, all values α and β of the sub-


Yangyang Tang
email: yangyang.tang@univ-ubs.fr

Emmanuel Boutillon

Chris Winstead

Christophe Jégo

Michel Jézéquel

Muller C-element based Decoder (MCD): A Decoder Against Transient Faults

This work extends the analysis and application of a digital error correction method called Muller C-element Decoding (MCD), which has been proposed for fault masking in logic circuits comprised of unreliable elements. The proposed technique employs cascaded Muller C-elements and XOR gates to achieve efficient error-correction in the presence of internal upsets. The error-correction analysis of MCD architecture and the investigation of C-element's robustness are first introduced. We demonstrate that the MCD is able to produce error-correction benefit in a high error-rate of internal faults. Significantly, for a (3,6) short-length Low Density Parity Check (LDPC) code, when the decoding process is internally error-free the MCD achieves also a gain in terms of decoding performance by comparison to the well-known Gallager Bit-Flipping method. We further consider application of MCD to a general-purpose fault-tolerant model, coded Dual Modular Redundancy (cDMR), which offers low-redundancy error-resilience for contemporary logic systems as well as future nanoeletronic architectures.

I. INTRODUCTION

Due to the rapid development of logic circuit manufacturing in the last two decades, electronic devices are now miniaturized to nanoscale dimensions. Nanoscale devices are increasingly sensitive to faults due to manufacturing defects, environmental fluctuations, and electronic noise or interference. From the circuit perspective, semiconductor faults fall into three main categories: permanent, intermittent, and transient. Permanent faults are caused by manufacturing defects, or device wear-out. They reflect irreversible physical changes. Intermittent faults occur because of unstable or marginal hardware; they can be activated and later reversed by environmental changes, like higher or lower temperature and voltage. Transient defects occur on a shorter time-scale, arising from device noise, interference or particle interactions. Due to the size downscaling processes, digital logic circuits are increasingly vulnerable to the transient faults [START_REF] Baumann | Soft errors in advanced semiconductor devices-part i: the three radiation sources[END_REF].

Since any embedded fault-masking solution is implemented using the same device as the logic it protects, it is important for a fault-masking technique to be also tolerant of internal errors within its own logic. Researchers previously investigated the performance of a variety of error-correcting schemes under the influence of intrinsic faults [START_REF] Shim | Energy-efficient soft error-tolerant digital signal processing[END_REF]- [START_REF] Yazdi | Optimal design of a gallager b noisy decoder for irregular ldpc codes[END_REF]. In many cases, the proposed fault-masking solutions are limited to particular applications or algorithms. For example, an Algorithmic Noise-Tolerance (ANT) technique was introduced by Shim et al., for reliable low-power digital signal processing [START_REF] Shim | Energy-efficient soft error-tolerant digital signal processing[END_REF]. The ANT method is based on a reduced precision replica to achieve low-power robust system in certain DSP algorithms. However, the ANT method is difficult to adapt if the reduced precision block cannot be done in an efficient way. An Error Resilient System Architecture (ERSA) [START_REF] Leem | Ersa: error resilient system architecture for probabilistic applications[END_REF] was proposed for low-cost robust systems, but incurs higher costs for general-purpose applications. Thus, the need of an efficient general-purpose fault-tolerant design is evident.

In the authors' previous work [START_REF] Tang | An ldpc decoding method for fault-tolerant digital logic[END_REF], [START_REF] Winstead | A spacetime redundancy technique for embedded stochastic error correction[END_REF], an error-correction method based on Muller C-elements was introduced and shown to be robust against internal transient faults. This method, referred as to MCD, is an implementation of iterative Low Density Parity Check (LDPC) [START_REF] Gallager | Low Density Parity Check Codes[END_REF] decoders suitable for embedding into digital logic circuits. The MCD method consists primarily of C-elements and XOR gates which implement a parity-check decoding algorithm. The MCD differs from traditional parity-check algorithms in that its circuit topology is designed to suppress internal upsets within the decoder.

In this paper, an extended work of MCD technique and its implementation for embedded robust design are detailed. The main contributions of this work are threefold: First the error-correction analysis of MCD is shown. Second, the study of error-resilience capacity inherited by C-element is detailed. Lastly, we study a coded Dual Modular Redundancy (cDMR) application with a short length MCD, which achieves a significant gain in terms of decoding performance for both error-free and noisy decoding cases.

II. BIT-FLIPPING METHOD AND MCD ARCHITECTURE

A. Gallager's Bit-Flipping Method LDPC decoding methods are traditionally described as message-passing on a code's Tanner graph [START_REF] Kschischang | Factor graphs and the sumproduct algorithm[END_REF]. The Tanner graph contains two sets of nodes -variable nodes v i and parity-check nodes p j . Some edges connect the variable nodes to the parity-check nodes thanks to a sparse parity-check matrix associated to each LDPC code. The degree of a node is the number of edges connected to it in the Tanner graph. Let d v be the degree of variable node v i , and let V i be the set of edges that are connected to v i . Similarly, let d c be the degree of parity-check node p j , and let P j be the set of edges that are connected to p j . During the decoding process, binary messages are exchanged between the two sets of nodes. The message passed from node v i to p j is written y ij , and the returning message from p j to v i is written f ji . All nodes are simple processing functions that follow the standard extrinsic information principle: the outgoing message on edge k is computed using information from all edges except k.

Gallager's Bit-Flipping Methods (GBF) were among the first LDPC decoding algorithms introduced by Gallager [START_REF] Gallager | Low Density Parity Check Codes[END_REF]. The GBF methods are defined for frames that were transmitted over a Binary Symmetric Channel (BSC), as a binary hard decision message-passing decoding method [START_REF] Richardson | The capacity of low-density paritycheck codes under message-passing decoding[END_REF]. A GBF algorithm can be described as follows. The variable nodes initially transmit messages y ij = x i for all i, j. For each parity-check node, the outgoing message on edge k is equal to the modulo-2 sum of all local incoming messages (excluding edge k). For the variable nodes, the outgoing message along edge k is equal to x i unless at least b incoming messages (excluding edge k) disagree with the x i . Traditionally, there are two versions of the algorithm. When b =(d v -1), all local incoming messages are required to be unanimous, the method is known as the Gallager-A algorithm. If b is fixed to a smallest integer during the decoding iteration as explained in [START_REF] Gallager | Low Density Parity Check Codes[END_REF] and [START_REF] Richardson | The capacity of low-density paritycheck codes under message-passing decoding[END_REF], then the method is known as the Gallager-B algorithm.

B. The MCD Architecture

The MCD architecture is characterized by the processing steps applied at the variable nodes. For each variable node v i , a set of C-element gates C k , 0 ≤ k<(d v -1), is associated as shown in Fig. 1(a) [START_REF] Tang | An ldpc decoding method for fault-tolerant digital logic[END_REF]. The circuit is a cascade of C-element gates, modified for the initialization of the state memory. In this figure, d v =4 . Each C-element has three inputs; the left-side inputs are the usual inputs, and the top-side input is the initial state for the C-element's memory. Each C-element gate C k contains a single-bit storage element c k . Moreover, a standard binary C-element circuit is shown in Fig. 1(b) [START_REF] Muller | A theory of asynchronous circuits[END_REF]. The MCD decoding algorithm is described as follows:

1) Initialize y k = x i , for all k ∈V.

2) Compute f ji = ⊕ m∈P j\i y mj for all j ∈P.

3) Initialize each C-element memory as

c k = f k ′ , where k ′ =(k + d v -1) mod d v . 4)
The C-element's port connections are as follows. For C 0 , the inputs are f 0 (f 0 = x i ) and f 1 , and the output is c 0 .F o rC k , the inputs are c k-1 and f k+1 , and the output is c k . 5) Iterate steps 2 and 4 during a fixed number of iterations, as the restoration phase. Note that the initialization in step 3 is performed only during the first iteration. 6) The corrected output is z i = c (dv-1) . This algorithm is guaranteed to correct a single error during each iteration. It can also correct many multi-error patterns as well [START_REF] Tang | An ldpc decoding method for fault-tolerant digital logic[END_REF], [START_REF] Winstead | A spacetime redundancy technique for embedded stochastic error correction[END_REF]. The MCD method can be regarded as a circuitlevel implementation for variable nodes in an LDPC decoder.

III. ERROR-CORRECTION ANALYSIS

An error obtained from f k may originate from an internal error within the decoder. The C-element cascade helps to stop the propagation of such errors. As the error-correction analysis done in [START_REF] Winstead | A spacetime redundancy technique for embedded stochastic error correction[END_REF], a single error event can be masked during an iteration. In the rest of this subsection we study the cases of double-error events in restoration phase during an iteration.

A. Double errors appear at f k and f l If a variable node v i receives two erroneous messages at f k and f l , such that |k -l|≥1, there are three possible cases:

• If f 0 and f 1 are erroneous, the output of C 0 is thus erroneous. Since the rest of f k and storages are correct, the error from C 0 is masked. • f 0 and f k (k>1) are incorrect. In this case, the output of C 0 is correct, and any erroneous f k can't induce an error event.

• f k and f l ,( k = l =0 ), are erroneous. In this case, any single error event is waived.

B. Double errors appear at c k and c l If a variable node v i generated two upsets at c k and c l , such that |k -l|≥1, these events can be sorted as a single error event occurrence. Consequently, these cases are masked by the inherent fault-tolerance by C-element.

C. Double errors appear at f k and c l

If two upsets occur at f k and c l of a variable node v i , where |k -l|≥0, three cases are possible:

• if k =( d v -1) and l =( d v -2)
, the value of Celement C l , c l , is correct. Since only single-error event is occurred among the C-elements except C l , due to Celement's behavior another input of C l is assured errorfree. In this case, only f k is erroneous that can not induce an error at the output.

• When k =( d v -1) and l =( d v -2), f k and c l are correct.
Hence, the output from v i is correct as well. • At last, if k =(d v -1) and l =(d v -2), f k and c l are thus incorrect. In this case, the output is erroneous. To sum up, a cascaded C-element set is able to correct any single error event regardless of where those errors originate. Any double-error events can be corrected, except a single pattern, namely the local incoming message to the last Celement and its storage are simultaneously flipped over. For the burst errors, the C-element set can also correct some patterns.

IV. FAULT-TOLERANCE INHERITED BY C-ELEMENT

To further reveal the error-resilience inherited from Celement, we study the reliability of a state memory of Celement by comparison to a static logic gate, namely an inverter. Without loss of generality, the state memory was designed for a 0.6μm CMOS logic process. For comparison, an inverter was also designed. Both circuits were simulated in Virtuoso Spectre from Cadence, where signal errors are set up in a large scale by the "noisescale" parameter. Fig. 2 shows an overlay of Monte Carlo transient simulation runs form both the state memory and the static gate simulations. The "noisescale" parameter is set as large scale in order to induce enough upset cases to measure and compare the error rate for those two components. An error occurs whenever the difference crosses 0.05V threshold when 5V as the correct output. More precisely, if the difference of output value to the correct one (5V ) is bigger than 0.05V , then an error is considered. The difference lower than 0.05V is bypassed. For the static gate, errors appear quite frequently as indicated by numerous threshold-crossings. By contrast, in the state memory case, the amplitude of output noise fluctuations is significantly cutoff. Thanks to the feedback mechanism in the state memory, up to a magnitude of two orders as the robustness gain. Consequently, by comparison to a static logic gate, C-element is able to tolerates the upset events with errorresilience gain between multiple times up to magnitude of two orders.

V. T HE CDMR TECHNIQUE BY APPLYING MCD

A. cDMR Technique

One of the authors (Winstead) proposed an LDPC-coded Fault Compensation Technique (LFCT) in [START_REF] Winstead | Probabilistic LDPC-coded fault compensation technique for reliable nanoscale computing[END_REF]. This technique is relevant to higher LDPC codes resulting in a more powerful error-correcting ability. With taking the principle of LFCT, a coded Dual-Modular Redundancy (cDMR) technique can be defined as shown in Fig. 3. More detailed can also be found in [START_REF] Tang | An ldpc decoding method for fault-tolerant digital logic[END_REF] and [START_REF] Winstead | A spacetime redundancy technique for embedded stochastic error correction[END_REF]. A logic function F (u) is implemented using a digital CMOS technology that is subject to errors at its output. The original function F (u) is augmented by the addition of a redundant parity-generator module, H • F (u), where H represents the encoding function that generates parity bits codeword space at the output of F (u) as explained in [START_REF] Winstead | Probabilistic LDPC-coded fault compensation technique for reliable nanoscale computing[END_REF]. The systematic output word s is then concatenated with the parity outputs r from H • F (u), yielding a complete codeword [sr]. According to the code's H matrix, namely the parity-check matrix that defines the error-correction code, an Error Control Codes (ECC) is supposed to perform the error-correction in the presence of internal faults.

B. Good Decoder Candidate for the ECC of cDMR

In this subsection, we demonstrate a good candidate for the ECC of cDMR. By comparison to the GBF approach, the performance improvement achieved with MCD was analyzed using two metrics: the BER performances over BSC under a error-free decoding process and faulty decoding process. For the sake of facility, only LDPC code with d v =3is studied.

A [START_REF] Leem | Ersa: error resilient system architecture for probabilistic applications[END_REF][START_REF] Tang | A new single-error correction scheme based on self-diagnosis residue number arithmetic[END_REF] LDPC code of length 64 was simulated over BSC in the cases of error-free and noisy decoding process, respectively, as shown in Fig. 4. First, in the case of noisy decoding as dashed curves, the GBF performance worsens with increased iterations, but MCD does not suffer from this degradation. Significantly, when the length of a LDPC code is short, the MCD performs a gain in terms of decoding performance, as shown the solid curves in Fig. 4. As such, this short MCD decoder is a good candidate to the ECC block. Consequently, with employing the MCD architecture, the cDMR technique that can prevent the internal upsets provides a general-purpose robust system to logic design. VI. DISCUSSION: CDMR'S IMPLEMENTATION To avoid the occurrence of correlated errors among s and r, the most reliable approach is regarded in two cases: if F (u) has low complexity, such like finite-state machines, F (u) and H • F (x) then can be easily designed without resulting correlated errors; if F (u) has a high complexity and large fanin and fanout, a flat truth-table synthesis can be used, as is done with cross-bar logic arrays [START_REF] Rao | Logic mapping in crossbar-based nanoarchitectures[END_REF]. To explain this constraint, we may contrast the two circuits shown in Fig. 5. In Fig. 5(a), a ripple-carry implementation, a single gate error may propagate to the several of the output signals. An example of error propagation is indicated by the symbol in Fig. 5(a). In the cDMR system, error-propagation may induce many simultaneous faults in the [sr ] codeword, which are not likely to be correctable. In the crossbar implementation, as shown in Fig. 5(b), logic is implemented by fabrics of AND-logic and OR-logic. The "dots" indicate the placement of junctions which physically implement the logic operations. In this style of implementation, every operation is associated with only a single output. If a momentary fault occurs at some junction, it will propagate only to a single output. This implementation guarantees that single-error events are correctable. The major disadvantage of crossbar logic is that the operation counts are not optimal. The crossbar adder in Fig. 5(b), for instance, is composed of 57 separate operations. Crossbar logic does not generally obtain minimized gate complexity, but it offers improved reliability by eliminating error propagations.

VII. CONCLUSION

The Muller C-element based Decoder, referred as to MCD, has been proposed for efficient error-correction in the presence of high error rate internal upsets. In this work, an extended study of MCD is presented. The error-correction analysis of MCD and the study of C-element's fault-tolerance are first introduced. By comparison to the well-known Gallager's Bit-Flipping method, for a (3,6) LDPC code of short length, the MCD yields a gain in terms of decoding performance in the cases of error-free and faulty decoding. At last, by applying the MCD, a coded Dual-Modular Redundancy (cDMR) technique designed for robust hard-on to current logic or future nanoelectronics is optimized.

Fig. 1 :

 1 Fig. 1: A local implementation of a variable node (a), and a standard Muller C-element circuit of which the state memory c k is realized by a weak-keeper (b).

Fig. 2 :

 2 Fig. 2: Simulated error rate results obtained using the 0.6μm CMOS model in Virtuoso Spectre.

Fig. 3 :

 3 Fig. 3: Architecture of the cDMR model.

Fig. 4 :

 4 Fig. 4: Simulation results of (3,6) LDPC code of length 64 under faulty and error-free decoding.

Fig. 5 :

 5 Fig. 5: Two-bit binary adder implementations, representing a traditional ripple-carry design (a), and a crossbar design suitable for some nanoelectronic device families (b).

ACKNOWLEDGMENT

This work was supported by the US National Science Foundation under award ECCS-0954747 and CCF-0916105.