Improving the Decoding of LDPC Codes for the Packet Erasure Channel with a Hybrid Zyablov Iterative Decoding/Gaussian Elimination Scheme

Mathieu Cunche 1 Vincent Roca 1
1 PLANETE - Protocols and applications for the Internet
Inria Grenoble - Rhône-Alpes, CRISAM - Inria Sophia Antipolis - Méditerranée
Abstract : This work focuses on the decoding algorithm of the LDPC large block FEC codes for the packet erasure channel, also called AL-FEC (Application-Level Forward Error Correction). More specifically this work details the design and the performance of a hybrid decoding scheme, that starts with the Zyablov iterative decoding algorithm, a rapid but suboptimal algorithm in terms of erasure recovery capabilities, and, when required, continues with a Gaussian elimination algorithm. For practical reasons this work focuses on two LDPC codes for the erasure channel, namely LDPC-staircase and LDPC-triangle codes. Nevertheless the decoding scheme proposed can be used with other LDPC codes without any problem. The performance experiments carried out show that the erasure recovery capabilities of LDPC-triangle codes are now extremely close to that of an ideal code, even with small block sizes. This is all the more true with small code rates: whereas the Zyablov iterative decoding scheme becomes unusable as the code rate decreases, the Gaussian elimination makes the LDPC-triangle codes almost ideal. In all the tests, when carefully implemented, the LDPC-triangle codec featuring the proposed decoding scheme is fast, and in particular always significantly faster than the reference Reed-Solomon on GF($2^{8}$) codec. The erasure recovery capabilities of LDPC-staircase codes are also significantly improved, even if they remain a little bit farther from an ideal code. Nevertheless, a great advantage is the fact that LDPC-staircase codes remain significantly faster than LDPC-triangle codes, which, for instance, enables their use with larger blocks. All these results make these codes extremely attractive for many situations and contradict the common belief that using Gaussian elimination is not usable because of a prohibitive processing load. Moreover the proposed approach offers an important flexibility in practice, and depending on the situation, one can either choose to favor erasure recovery capabilities or the processing time.
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Rapport
[Research Report] RR-6473, INRIA. 2008, pp.19
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Mathieu Cunche, Vincent Roca. Improving the Decoding of LDPC Codes for the Packet Erasure Channel with a Hybrid Zyablov Iterative Decoding/Gaussian Elimination Scheme. [Research Report] RR-6473, INRIA. 2008, pp.19. 〈inria-00263682v2〉

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