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.
Recently, two independent works @cite_12 @cite_13 proposed a hybrid iterative-ML decoding algorithm, where ML decoding is only used when the iterative decoding does not succeed to decode a received codeword.
@cite_13 @cite_12
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The design of low-density parity-check (LDPC) codes under hybrid iterative maximum likelihood decoding is addressed for the binary erasure channel (BEC). Specifically, we focus on generalized irregular repeat-accumulate (GeIRA) codes, which offer both efficient encoding and design flexibility. We show that properly designed GeIRA codes tightly approach the performance of an ideal maximum distance separable (MDS) code, even for short block sizes. For example, our (2048,1024) code reaches a codeword error rate of 10-5 at channel erasure probability isin= 0.450, where an ideal (2048,1024) MDS code would reach the same error rate at isin = 0.453. 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( @math ) 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.