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

Phong S. Nguyen, Henry D. Pfister, Krishna R. Narayanan
2009 2009 47th Annual Allerton Conference on Communication, Control, and Computing (Allerton)  
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-versuscomplexity trade-off of multiple error-and-erasure decoding of RS codes. By defining an appropriate distortion measure between an error pattern and an
more » ... e 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.
doi:10.1109/allerton.2009.5394533 fatcat:jxpyo7sppvaq5eiszznfgjjkd4