A Low-Complexity Method for Chase-Type Decoding of Reed-Solomon Codes

In this work we present a low-complexity implementation of Chase-type decoding of Reed-Solomon Codes. In such, we first use the soft-information available at the channel output to construct a test-set of 2^η vectors, equival ent in all except the η << n least reliable coordinate positions. We then give an interpolation procedure to construct a set of 2^η bivariate polynomials, with the roots of each specified by its corresponding test-vector. Here, test-vector similarity is exploited to share much of the required computation. Finally, we obtain the candidate message from the single z-linear factor of each bivariate polynomial. Although we provide an expression for the direct computation of each candidate message, the complexity of repeating this computation for each interpolation polynomial is prohibitive. We, thus, also present a reduced-complexity factorization (RCF) method to select a single polynomial that, with high probability, contains the correctly decoded message in its z-linear factor. Although suboptimal, the loss in performance of RCF decreases rapidly with increasing code length. We provide extensive simulation results showing that a significant performance increase over traditional hard-decision decoding is achievable with a comparable computational complexity (as implemented with the Berlekamp-Massey Algorithm).