Generalized IRA Erasure Correcting Codes for Hybrid Iterative / Maximum Likelihood Decoding

Abstract

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, also for short block sizes. For example, our (2048, 1024) code reaches a codeword error rate of 10e-5 at channel erasure probability epsilon=0.450, where an ideal code would reach the same error rate for epsilon=0.453.