Fast Reliability-based Algorithm of Finding Minimum-weight Codewords for LDPC Codes

摘要

Despite the NP hardness of acquiring minimum distance $d_m$ for linear codestheoretically, in this paper we propose one experimental method of findingminimum-weight codewords, the weight of which is equal to $d_m$ for LDPC codes.One existing syndrome decoding method, called serial belief propagation (BP)with ordered statistic decoding (OSD), is adapted to serve our purpose. We holdthe conjecture that among many candidate error patterns in OSD reprocessing,modulo 2 addition of the lightest error pattern with one of the left errorpatterns may generate a light codeword. When the decoding syndrome changes toall-zero state, the lightest error pattern reduces to all-zero, the lightestnon-zero error pattern is a valid codeword to update lightest codeword list. Given sufficient codewords sending, the survived lightest codewords arelikely to be the target. Compared with existing techniques, our methoddemonstrates its efficiency in the simulation of several interested LDPC codes.