A rate-distortion perspective on multiple decoding attempts for Reed-Solomon codes

Recently, a number of authors have proposed decoding schemes for Reed-Solomon (RS) codes based on multiple trials of a simple RS decoding algorithm. In this paper, we present a rate-distortion (R-D) approach to analyze these multiple-decoding algorithms for RS codes. This approach is first used to understand the asymptotic performance-versus-complexity trade-off of multiple error-and-erasure decoding of RS codes. By defining an appropriate distortion measure between an error pattern and an erasure pattern, the condition for a single error-and-erasure decoding to succeed reduces to a form where the distortion is compared to a fixed threshold. Finding the best set of erasure patterns for multiple decoding trials then turns out to be a covering problem which can be solved asymptotically by rate-distortion theory. Next, this approach is extended to analyze multiple algebraic soft-decision (ASD) decoding of RS codes. Both analytical and numerical computations of the R-D functions for the corresponding distortion measures are discussed. Simulation results show that proposed algorithms using this approach perform better than other algorithms with the same complexity.