Decoding of Convolutional Codes over the Erasure Channel

In this paper we study the decoding capabilities of convolutional codes over the erasure channel. Of special interest will be maximum distance profile (MDP) convolutional codes. These are codes which have a maximum possible column distance increase. We show how this strong minimum distance condition of MDP convolutional codes help us to solve error situations that maximum distance separable (MDS) block codes fail to solve. Towards this goal, we define two subclasses of MDP codes: reverse-MDP convolutional codes and complete-MDP convolutional codes. Reverse-MDP codes have the capability to recover a maximum number of erasures using an algorithm which runs backward in time. Complete-MDP convolutional codes are both MDP and reverse-MDP codes. They are capable to recover the state of the decoder under the mildest condition. We show that complete-MDP convolutional codes perform in certain sense better than MDS block codes of the same rate over the erasure channel.Comment: 18 pages, 3 figures, to appear on IEEE Transactions on Information Theor

List decoding of Convolutional Codes over integer residue rings

A convolutional code \C over \ZZ[D] is a \ZZ[D]-submodule of \ZZN[D] where \ZZ[D] stands for the ring of polynomials with coefficients in \ZZ. In this paper, we study the list decoding problem of these codes when the transmission is performed over an erasure channel, that is, we study how much information one can recover from a codeword w\in \C when some of its coefficients have been erased. We do that using the $p$-adic expansion of $w$ and particular representations of the parity-check polynomial matrix of the code. From these matrix polynomial representations we recursively select certain equations that $w$ must satisfy and have only coefficients in the field p^{r-1}\ZZ. We exploit the natural block Toeplitz structure of the sliding parity-check matrix to derive a step by step methodology to obtain a list of possible codewords for a given corrupted codeword $w$, that is, a list with the closest codewords to $w$

Concatenation of convolutional codes and rank metric codes for multi-shot network coding

In this paper we present a novel coding approach to deal with the transmission of information over a network. In particular we make use of the network several times (multishot)and impose correlation in the information symbols over time. We propose to encode the information via an inner and an outer code, namely, a Hamming metric convolutional code as an outer code and a rank metric code as an inner code. We show how this simple concatenation scheme can exploit the potential of both codes to produce a code that can correct a large number of error patterns

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