Improved List Decoding of Generalized Reed–Solomon and Alternant Codes Over Galois Rings
M.A. Armand · IEEE Transactions on Information Theory · 2005
We present a two-stage list decoder comprising an errors-only Guruswami-Sudan (GS) decoder and an errors-and-erasures GS decoder as component decoders in the first and second stage, respectively. The two stages are coupled via a post-processor which selects a codeword from the output list of the first component decoder, from which erasure locations are obtained for the second stage. When applied to a generalized Reed-Solomon (RS) code over a Galois ring R that maps into a generalized RS code of the same length n and minimum (Hamming) distance d over the corresponding residue field, the proposed decoder exploits the presence of zero divisors in R to correct s errors where w=lceiln-radic(n(n-d))-1rceill), an important class of subring subcodes of generalized RS codes over GR(2l,a), we demonstrate that the GS decoding radius w can be exceeded by a substantial margin with significant probability