Analysis and Design of Finite Alphabet Iterative Decoders Robust to Faulty Hardware

This paper addresses the problem of designing LDPC decoders robust to transient errors introduced by a faulty hardware. We assume that the faulty hardware introduces errors during the message passing updates and we propose a general framework for the definition of the message update faulty functions. Within this framework, we define symmetry conditions for the faulty functions, and derive two simple error models used in the analysis. With this analysis, we propose a new interpretation of the functional Density Evolution threshold previously introduced, and show its limitations in case of highly unreliable hardware. However, we show that under restricted decoder noise conditions, the functional threshold can be used to predict the convergence behavior of FAIDs under faulty hardware. In particular, we reveal the existence of robust and non-robust FAIDs and propose a framework for the design of robust decoders. We finally illustrate robust and non-robust decoders behaviors of finite length codes using Monte Carlo simulations.Comment: 30 pages, submitted to IEEE Transactions on Communication

Density Evolution and Functional Threshold for the Noisy Min-Sum Decoder

This paper investigates the behavior of the Min-Sum decoder running on noisy devices. The aim is to evaluate the robustness of the decoder in the presence of computation noise, e.g. due to faulty logic in the processing units, which represents a new source of errors that may occur during the decoding process. To this end, we first introduce probabilistic models for the arithmetic and logic units of the the finite-precision Min-Sum decoder, and then carry out the density evolution analysis of the noisy Min-Sum decoder. We show that in some particular cases, the noise introduced by the device can help the Min-Sum decoder to escape from fixed points attractors, and may actually result in an increased correction capacity with respect to the noiseless decoder. We also reveal the existence of a specific threshold phenomenon, referred to as functional threshold. The behavior of the noisy decoder is demonstrated in the asymptotic limit of the code-length -- by using "noisy" density evolution equations -- and it is also verified in the finite-length case by Monte-Carlo simulation.Comment: 46 pages (draft version); extended version of the paper with same title, submitted to IEEE Transactions on Communication

Source Coding with Side Information at the Decoder and Uncertain Knowledge of the Correlation

International audienceThis paper considers the problem of lossless source coding with side information at the decoder, when the correlation model between the source and the side information is uncertain. Four parametrized models representing the correlation between the source and the side information are introduced. The uncertainty on the correlation appears through the lack of knowledge on the value of the parameters. For each model, we propose a practical coding scheme based on non-binary Low Density Parity Check Codes and able to deal with the parameter uncertainty. At the encoder, the choice of the coding rate results from an information theoretical analysis. Then we propose decoding algorithms that jointly estimate the source vector and the parameters. As the proposed decoder is based on the Expectation-Maximization algorithm, which is very sensitive to initialization, we also propose a method to produce first a coarse estimate of the parameters

Density Evolution for the Design of Non-Binary Low Density Parity Check Codes for Slepian-Wolf Coding

International audienceIn this paper, we investigate the problem of designing good non-binary LDPC codes for Slepian-Wolf coding. The design method is based on Density Evolution which gives the asymptotic error probability of the decoder for given code degree distributions. Density Evolution was originally introduced for channel coding under the assumption that the channel is symmetric. In Slepian-Wolf coding, the correlation channel is not necessarily symmetric and the source distribution has to be taken into account. In this paper, we express the non-binary Density Evolution recursion for Slepian-Wolf coding. From Density Evolution, we then perform code degree distribution optimization using an optimization algorithm called differential evolution. Both asymptotic performance evaluation and finite-length simulations show the gain at considering optimized degree distributions for SW coding

Codage Distribué dans des Réseaux de Capteurs avec Connaissance Incertaine des Corrélations

National audienceCet article aborde le problème du codage d'une source X avec information adjacente Y disponible uniquement au décodeur dans le cas où P(Y|X) est mal connue au décodeur

Codage de sources avec information adjacente et connaissance incertaine des corrélations

Dans cette thèse, nous nous sommes intéressés au problème de codage de sources avec information adjacente au décodeur seulement. Plus précisément, nous avons considéré le cas où la distribution jointe entre la source et l'information adjacente n'est pas bien connue. Dans ce contexte, pour un problème de codage sans pertes, nous avons d'abord effectué une analyse de performance à l'aide d'outils de la théorie de l'information. Nous avons ensuite proposé un schéma de codage pratique efficace malgré le manque de connaissance sur la distribution de probabilité jointe. Ce schéma de codage s'appuie sur des codes LDPC non-binaires et sur un algorithme de type Espérance-Maximisation. Le problème du schéma de codage proposé, c'est que les codes LDPC non-binaires utilisés doivent être performants. C'est à dire qu'ils doivent être construits à partir de distributions de degrés qui permettent d'atteindre un débit proche des performances théoriques. Nous avons donc proposé une méthode d'optimisation des distributions de degrés des codes LDPC. Enfin, nous nous sommes intéressés à un cas de codage avec pertes. Nous avons supposé que le modèle de corrélation entre la source et l'information adjacente était décrit par un modèle de Markov caché à émissions Gaussiennes. Pour ce modèle, nous avons également effectué une analyse de performance, puis nous avons proposé un schéma de codage pratique. Ce schéma de codage s'appuie sur des codes LDPC non-binaires et sur une reconstruction MMSE. Ces deux composantes exploitent la structure avec mémoire du modèle de Markov caché.In this thesis, we considered the problem of source coding with side information available at the decoder only. More in details, we considered the case where the joint distribution between the source and the side information is not perfectly known. In this context, we performed a performance analysis of the lossless source coding scheme. This performance analysis was realized from information theory tools. Then, we proposed a practical coding scheme able to deal with the uncertainty on the joint probability distribution. This coding scheme is based on non-binary LDPC codes and on an Expectation-Maximization algorithm. For this problem, a key issue is to design efficient LDPC codes. In particular, good code degree distributions have to be selected. Consequently, we proposed an optimization method for the selection of good degree distributions. To finish, we considered a lossy coding scheme. In this case, we assumed that the correlation channel between the source and the side information is described by a Hidden Markov Model with Gaussian emissions. For this model, we performed again some performance analysis and proposed a practical coding scheme. The proposed scheme is based on non-binary LDPC codes and on MMSE reconstruction using an MCMC method. In our solution, these two components are able to exploit the memory induced by the Hidden Markov model.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Transmission and Storage Rates for Sequential Massive Random Access

This paper introduces a new source coding paradigm called Sequential Massive Random Access (SMRA). In SMRA, a set of correlated sources is encoded once for all and stored on a server, and clients want to successively access to only a subset of the sources. Since the number of simultaneous clients can be huge, the server is only allowed to extract a bitstream from the stored data: no re-encoding can be performed before the transmission of the specific client's request. In this paper, we formally define the SMRA framework and introduce both storage and transmission rates to characterize the performance of SMRA. We derive achievable transmission and storage rates for lossless source coding of i.i.d. and non i.i.d. sources, and transmission and storage rates-distortion regions for Gaussian sources. We also show two practical implementations of SMRA systems based on rate-compatible LDPC codes. Both theoretical and experimental results demonstrate that SMRA systems can reach the same transmission rates as in traditional point to point source coding schemes, while having a reasonable overhead in terms of storage rate. These results constitute a breakthrough for many recent data transmission applications in which different parts of the data are requested by the clients

The Recent Evolution of a Maternally-Inherited Endosymbiont of Ticks Led to the Emergence of the Q Fever Pathogen, Coxiella burnetii

International audienceQ fever is a highly infectious disease with a worldwide distribution. Its causative agent, the intracellular bacterium Coxiella burnetii, infects a variety of vertebrate species, including humans. Its evolutionary origin remains almost entirely unknown and uncertainty persists regarding the identity and lifestyle of its ancestors. A few tick species were recently found to harbor maternally-inherited Coxiella-like organisms engaged in symbiotic interactions, but their relationships to the Q fever pathogen remain unclear. Here, we extensively sampled ticks, identifying new and atypical Coxiella strains from 40 of 58 examined species, and used this data to infer the evolutionary processes leading to the emergence of C. burnetii. Phylogenetic analyses of multi-locus typing and whole-genome sequencing data revealed that Coxiella-like organisms represent an ancient and monophyletic group allied to ticks. Remarkably, all known C. burnetii strains originate within this group and are the descendants of a Coxiella-like progenitor hosted by ticks. Using both colony-reared and field-collected gravid females, we further establish the presence of highly efficient maternal transmission of these Coxiella-like organisms in four examined tick species, a pattern coherent with an endosymbiotic lifestyle. Our laboratory culture assays also showed that these Coxiella-like organisms were not amenable to culture in the vertebrate cell environment, suggesting different metabolic requirements compared to C. burnetii. Altogether, this corpus of data demonstrates that C. burnetii recently evolved from an inherited symbiont of ticks which succeeded in infecting vertebrate cells, likely by the acquisition of novel virulence factors