Spatial Implementation for Erasure Coding by Finite Radon Transform

International audienceFault-tolerance has been widely studied these years in order to fit new kinds of applications running on unreliable systems such as the Internet. Erasure coding aims at recovering information that has been lost during a transmission (e.g. congestion). Considered as the alternative to the Automatic Repeat-reQuest (ARQ) strategy, erasure coding differs by adding redundancy to recover lost information without the need to retransmit data. In this paper we propose a new approach using the Finite Radon Transform (FRT). The FRT is an exact and discrete transformation that relies on simple additions to obtain a set of projections. The proposed erasure code is Maximal Distance Separable (MDS). We detail in this paper the systematic and nonsystematic implementation. As an optimization, we use the same algorithm called "row-solving" for creating the redundancy and for recovering missing data

Asymptotically MDS Array BP-XOR Codes

Belief propagation or message passing on binary erasure channels (BEC) is a low complexity decoding algorithm that allows the recovery of message symbols based on bipartite graph prunning process. Recently, array XOR codes have attracted attention for storage systems due to their burst error recovery performance and easy arithmetic based on Exclusive OR (XOR)-only logic operations. Array BP-XOR codes are a subclass of array XOR codes that can be decoded using BP under BEC. Requiring the capability of BP-decodability in addition to Maximum Distance Separability (MDS) constraint on the code construction process is observed to put an upper bound on the maximum achievable code block length, which leads to the code construction process to become a harder problem. In this study, we introduce asymptotically MDS array BP-XOR codes that are alternative to exact MDS array BP-XOR codes to pave the way for easier code constructions while keeping the decoding complexity low with an asymptotically vanishing coding overhead. We finally provide and analyze a simple code construction method that is based on discrete geometry to fulfill the requirements of the class of asymptotically MDS array BP-XOR codes.Comment: 8 pages, 4 figures, to be submitte

Asymptotically MDS Array BP-XOR Codes

Belief propagation or message passing on binary erasure channels (BEC) is a low complexity decoding algorithm that allows the recovery of message symbols based on bipartite graph prunning process. Recently, array XOR codes have attracted attention for storage systems due to their burst error recovery performance and easy arithmetic based on Exclusive OR (XOR)-only logic operations. Array BP-XOR codes are a subclass of array XOR codes that can be decoded using BP under BEC. Requiring the capability of BP-decodability in addition to Maximum Distance Separability (MDS) constraint on the code construction process is observed to put an upper bound on the maximum achievable code block length, which leads to the code construction process to become a harder problem. In this study, we introduce asymptotically MDS array BP-XOR codes that are alternative to exact MDS array BP-XOR codes to pave the way for easier code constructions while keeping the decoding complexity low with an asymptotically vanishing coding overhead. We finally provide and analyze a simple code construction method that is based on discrete geometry to fulfill the requirements of the class of asymptotically MDS array BP-XOR codes.Comment: 8 pages, 4 figures, to be submitte

QoE enhancement for H.264/SVC video transmission in MANET using MP-OLSR protocol

International audienceThis paper addresses the problem of enhancing video service quality for Mobile Ad Hoc Networks (MANET) scenarios. We offer Multipath Optimized Link State (MP-OLSR) routing protocol for H.264/SVC bitstream forwarding in the MANET network. Besides the usage of a suitable routing protocol, the video quality can be further enhanced by using the scalable encoding feature of Scalable Video Coding (SVC) combined with Unequal Error Protection (UEP). SVC is an extension of the H.264/AVC video compression standard used for high-quality video bitstreams encoding, providing spatial, temporal and quality scalability. To evaluate video quality, the Video Quality Metric (VQM) is used. We chose 5 different video contents for our simulations characterized by various temporal and spatial complexities. These video references are taken from the Video Quality Expert Group (VQEG). The results show that multipath routing combined with UEP can effectively improve the quality of video communication over MANET in terms of VQM and successful video decoding

Recovering missing slices of the discrete fourier transform using ghosts

The discrete Fourier transform (DFT) underpins the solution to many inverse problems commonly possessing missing or unmeasured frequency information. This incomplete coverage of the Fourier space always produces systematic artifacts called Ghosts. In this paper, a fast and exact method for deconvolving cyclic artifacts caused by missing slices of the DFT using redundant image regions is presented. The slices discussed here originate from the exact partitioning of the Discrete Fourier Transform (DFT) space, under the projective Discrete Radon Transform, called the discrete Fourier slice theorem. The method has a computational complexity of O(n\log-{2}n) (for an n=N\times N image) and is constructed from a new cyclic theory of Ghosts. This theory is also shown to unify several aspects of work done on Ghosts over the past three decades. This paper concludes with an application to fast, exact, non-iterative image reconstruction from a highly asymmetric set of rational angle projections that give rise to sets of sparse slices within the DFT

Optical computing by injection-locked lasers

A programmable optical computer has remained an elusive concept. To construct a practical computing primitive equivalent to an electronic Boolean logic, one should find a nonlinear phenomenon that overcomes weaknesses present in many optical processing schemes. Ideally, the nonlinearity should provide a functionally complete set of logic operations, enable ultrafast all-optical programmability, and allow cascaded operations without a change in the operating wavelength or in the signal encoding format. Here we demonstrate a programmable logic gate using an injection-locked Vertical-Cavity Surface-Emitting Laser (VCSEL). The gate program is switched between the AND and the OR operations at the rate of 1 GHz with Bit Error Ratio (BER) of 10e-6 without changes in the wavelength or in the signal encoding format. The scheme is based on nonlinearity of normalization operations, which can be used to construct any continuous complex function or operation, Boolean or otherwise.Comment: 47 pages, 7 figures in total, 2 tables. Intended for submission to Nature Physics within the next two week

Comparison of Channels: Criteria for Domination by a Symmetric Channel

This paper studies the basic question of whether a given channel $V$ can be dominated (in the precise sense of being more noisy) by a $q$-ary symmetric channel. The concept of "less noisy" relation between channels originated in network information theory (broadcast channels) and is defined in terms of mutual information or Kullback-Leibler divergence. We provide an equivalent characterization in terms of $\chi^2$-divergence. Furthermore, we develop a simple criterion for domination by a $q$-ary symmetric channel in terms of the minimum entry of the stochastic matrix defining the channel $V$. The criterion is strengthened for the special case of additive noise channels over finite Abelian groups. Finally, it is shown that domination by a symmetric channel implies (via comparison of Dirichlet forms) a logarithmic Sobolev inequality for the original channel.Comment: 31 pages, 2 figures. Presented at 2017 IEEE International Symposium on Information Theory (ISIT

Le code à effacement Mojette : Applications dans les réseaux et dans le Cloud

Dans ce travail, je présente l'intérêt du code correcteur à effacement Mojette pour des architectures de stockage distribuées tolérantes aux pannes. De manière générale, l'approche par code permet de réduire d'un facteur 2 le volume de données stockées par rapport à l'approche standard par réplication qui consiste à copier la donnée en autant de fois que l'on suppose de pannes. De manière spécifique, le code à effacement Mojette présente les performances requises pour la lecture et l'écriture de données chaudes i.e très régulièrement sollicitées. Ces performances en entrées/sorties permettent par exemple l'exécution de machines virtuelles sur des données distribuées par le système de fichier RozoFS. En outre, j'effectue un rappel de mes contributions dans le domaine des réseaux auto-organisés de type P2P et ad hoc mobile en présentant respectivement les protocoles P2PWeb et MP-OLSR. L'ensemble de ce travail est le fruit de 5 encadrements doctoraux et de 3 projets collaboratifs majeurs