Performance of Adaptive Belief Propagation Decoding and Maximum-Likelihood Bounds for Reed–Solomon Codes on Partial-Response Channels

In this paper, we examine the performance of the adaptive belief propagation (ABP) algorithm for decoding Reed-Solomon (RS) codes in conjunction with various partial-response channels used in magnetic recording. We compare the performance of the ABP decoder against the performance of standard hard-decision decoding and against the maximum-likelihood (ML) bounds. We also study the performance of an idealized version of the ABP decoder, one with perfect identification of "good" versus "bad" bits in the codeword. For typical RS codes, we find actual ABP performance about half a decibel worse than the ideal ABP, but even ideal ABP fails to achieve the ML bound by at least 1 dB