Rethinking reliability for long-delay networks

Delay Tolerant Networking (DTN) is currently an open research area following the interest of space companies in the deployment of Internet protocols for the space Internet. Thus, these last years have seen an increase in the number of DTN protocol proposals such as Saratoga or LTP-T. However, the goal of these protocols are more to send much error-free data during a short contact time rather than operating to a strictly speaking reliable data transfer. Beside this, several research work have proposed efficient acknowledgment schemes based on the SNACK mechanism. However, these acknowledgement strategies are not compliant with the DTN protocol principle. In this paper, we propose a novel reliability mechanism with an implicit acknowledgment strategy that could be used either within these new DTN proposals or in the context of multicast transport protocols. This proposal is based on a new erasure coding concept specifically designed to operate efficient reliable transfer over bi-directional links

Cokernels of random matrices satisfy the Cohen-Lenstra heuristics

Let A be an n by n random matrix with iid entries taken from the p-adic integers or Z/NZ. Then under mild non-degeneracy conditions the cokernel of A has a universal probability distribution. In particular, the p-part of an iid random matrix over the integers has cokernel distributed according to the Cohen-Lenstra measure up to an exponentially small error.Comment: 21 pages; submitte

Tetrys : Un mécanisme de fiabilisation polyvalent

Actuellement, une succession d’erreurs qui ne peut être masquée par le mécanisme de fiabilisation (code à effacement) doit attendre au minimum un RTT pour être corrigée, ce qui n’est souvent pas satisfaisant pour les application temps-réel. Les concepts apportés par la théorie du codage réseau (Network Coding) permettent aujourd’hui de combler le fossé entre fiabilisation et fiabilité totale en s'abstrayant du concept d’ARQ. Cet article présente un mécanisme innovant nommé Tetrys dont l’une des caractéristiques est de pouvoir reconstruire les pertes dans un temps paramétrable et indépendant du RTT. A notre meilleure connaissance, c'est la première fois que les propriétés temps réel d'un tel mécanisme sont énoncées et étudiées. Intuitivement, les applications ciblées sont celles nécessitant une fiabilité totale avec contrainte de délai. Il s’avère qu’à taux de redondance égal, des applications telles que la VoIP et la vidéo-conférence sont bien plus performantes lorsque les flux sont protégés par le mécanisme Tetrys que par les mécanismes FEC ou H-ARQ classiques. Après un rapide rappel des points clés relatifs à FEC et H-ARQ, nous décrivons le principe de Tetrys et montrons son possible déploiement. Nous comparons les performances de FEC, H-ARQ et Tetrys du point de vue applicatif à l'aide d’un prototype et suivant des métriques de délai et dans le cadre de la VoIP, de qualité de la transmission (MOS)

Approximate Decoding Approaches for Network Coded Correlated Data

This paper considers a framework where data from correlated sources are transmitted with help of network coding in ad-hoc network topologies. The correlated data are encoded independently at sensors and network coding is employed in the intermediate nodes in order to improve the data delivery performance. In such settings, we focus on the problem of reconstructing the sources at decoder when perfect decoding is not possible due to losses or bandwidth bottlenecks. We first show that the source data similarity can be used at decoder to permit decoding based on a novel and simple approximate decoding scheme. We analyze the influence of the network coding parameters and in particular the size of finite coding fields on the decoding performance. We further determine the optimal field size that maximizes the expected decoding performance as a trade-off between information loss incurred by limiting the resolution of the source data and the error probability in the reconstructed data. Moreover, we show that the performance of the approximate decoding improves when the accuracy of the source model increases even with simple approximate decoding techniques. We provide illustrative examples about the possible of our algorithms that can be deployed in sensor networks and distributed imaging applications. In both cases, the experimental results confirm the validity of our analysis and demonstrate the benefits of our low complexity solution for delivery of correlated data sources

Stein's method and the rank distribution of random matrices over finite fields

With ${\mathcal{Q}}_{q,n}$ the distribution of $n$ minus the rank of a matrix chosen uniformly from the collection of all $n\times(n+m)$ matrices over the finite field $\mathbb{F}_q$ of size $q\ge2$, and ${\mathcal{Q}}_q$ the distributional limit of ${\mathcal{Q}}_{q,n}$ as $n\rightarrow\infty$, we apply Stein's method to prove the total variation bound $\frac{1}{8q^{n+m+1}}\leq\|{\mathcal{Q}}_{q,n}-{\mathcal{Q}}_q\|_{\mathrm{TV}}\leq\frac{3}{q^{n+m+1}}$. In addition, we obtain similar sharp results for the rank distributions of symmetric, symmetric with zero diagonal, skew symmetric, skew centrosymmetric and Hermitian matrices.Comment: Published at http://dx.doi.org/10.1214/13-AOP889 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

On-the-fly erasure coding for real-time video applications

This paper introduces a robust point-to-point transmission scheme: Tetrys, that relies on a novel on-the-fly erasure coding concept which reduces the delay for recovering lost data at the receiver side. In current erasure coding schemes, the packets that are not rebuilt at the receiver side are either lost or delayed by at least one RTT before transmission to the application. The present contribution aims at demonstrating that Tetrys coding scheme can fill the gap between real-time applications requirements and full reliability. Indeed, we show that in several cases, Tetrys can recover lost packets below one RTT over lossy and best-effort networks. We also show that Tetrys allows to enable full reliability without delay compromise and as a result: significantly improves the performance of time constrained applications. For instance, our evaluations present that video-conferencing applications obtain a PSNR gain up to 7dB compared to classic block-based erasure codes