Achieving a near-optimum erasure correction performance with low-complexity LDPC codes

SUMMARY Low-density parity-check (LDPC) codes are shown to tightly approach the performance of idealized maximum distance separable (MDS) codes over memoryless erasure channels, under maximum likelihood (ML) decoding. This is possible down to low error rates and even for small and moderate block sizes. The decoding complexity of ML decoding is kept low thanks to a class of decoding algorithms, which exploit the sparseness of the parity-check matrix to reduce the complexity of Gaussian elimination. ML decoding of LDPC codes is reviewed at first. A performance comparison among various classes of LDPC codes is then carried out, including a comparison with fixed-rate Raptor codes for the same parameters. The results confirm that a judicious LDPC code design allows achieving a near-optimum performance over the erasure channel, with very low error floors. Furthermore, it is shown that LDPC and Raptor codes, under ML decoding, provide almost identical performance in terms of decoding failure probability vs. overhead.