2009/08/19 by Phong S. Nguyen, Henry D. Pfister, Nguyen, Phong S. +3
Computer Science · #Coding theory and cryptography #Cryptographic Implementations and Security #Error Correcting Code Techniques #FOS: Computer and information sciences #Information Theory (cs.IT)
paper · pdf · doi:10.48550/arxiv.0908.2828
openalex publication_date 2009/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.