BM-based fast chase decoding of binary BCH codes through degenerate list decoding

摘要

An application specific integrated circuit (ASIC) tangibly encodes a method for fast polynomial updates in fast Chase decoding of binary Bose-Chaudhuri-Hocquenghem (BCH) codes. The method includes the steps of using outputs of a syndrome-based hard-decision (HD) algorithm to find a Groebner basis for a solution module of a modified key equation, upon failure of HD decoding of a BCH codeword received by the ASIC from a communication channel; evaluating polynomials obtained from said Groebner basis at inverses of specified weak-bit locations; and transforming a Groebner basis for a set of flipped weak-bit locations (α₁, . . . , α_r−1) to a Groebner basis for (α₁, . . . , α_r), wherein α_r is a next weak-bit location, wherein r is a difference between a number of errors and a HD correction radius of the BCH codeword.