Abstract — This work focuses on the LDPC codes for the packet erasure channel, also called AL-FEC (Application-Level Forward Error Correction codes). Previous work has shown that the erasure recovery capabilities of LDPC-triangle and LDPCstaircase AL-FEC codes can be greatly improved by means of a Gaussian Elimination (GE) decoding scheme, possibly coupled to a preliminary Zyablov Iterative Decoding (ID) scheme. Thanks to the GE decoding, the LDPC-triangle codes were very close to an ideal code. If the LDPC-staircase performances were also improved, they were not as close to an ideal code as the LDPCtriangle codes were. The first goal of this work is to reduce the gap between the LDPC-staircase codes and the theoretical limit. We show that a simple modification of the parity check matrix can significantly improve their recovery capabilities when using a GE decoding. Unfortunately the performances of the same codes featuring an ID are negatively impacted, as well as the decoding complexity. The second goal of this work is therefore to find an appropriate balance between all these aspects. Index Terms — AL-FEC codes, erasure channel, LDPCstaircase, hybrid iterative decoding/Gaussian elimination I.

Abstract—This paper presents new FEC codes for the erasure channel, LDPC-Band, that have been designed so as to optimize a hybrid iterative-Maximum Likelihood (ML) decoding. Indeed, these codes feature simultaneously a sparse parity check matrix, which allows an efficient use of iterative LDPC decoding, and a generator matrix with a band structure, which allows fast ML decoding on the erasure channel. The combination of these two decoding algorithms leads to erasure codes achieving a very good trade-off between complexity and erasure correction capability. I. INTRODUCTION AND RELATED WORKS For the transmission of data packets on erasure channels, linear binary FEC codes often offer the best compromise between fast encoding/decoding operations and a good level of erasure recovery capability. For example, random binary codes

In this paper we propose a low-rate coding method, suited for application-layer forward error correction. Depending on channel conditions, the coding scheme we propose can switch from a fixed-rate LDPC code to various low-rate GLDPC codes. The source symbols are first encoded by using a staircase or triangular LDPC code. If additional symbols are needed, the encoder is then switched to the GLDPC mode and extra-repair symbols are produced, on demand. In order to ensure small overheads, we consider irregular distributions of extra-repair symbols optimized by density evolution techniques. We also show that increasing the number of extra-repair symbols improves the successful decoding probability, which becomes very close to 1 for sufficiently many extra-repair symbols.

Abstract not found

apport de recherche

c t i v it y e p o r t 2007 Table of contents

c t i v it y e p o r t 2008 Table of contents

apport de recherche

apport de recherche

Abstract not found