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Fast Reliability-based Algorithm of Finding Minimum-weight Codewords for LDPC Codes
Despite the NP hardness of acquiring minimum distance for linear codes
theoretically, in this paper we propose one experimental method of finding
minimum-weight codewords, the weight of which is equal to 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 hold
the conjecture that among many candidate error patterns in OSD reprocessing,
modulo 2 addition of the lightest error pattern with one of the left error
patterns may generate a light codeword. When the decoding syndrome changes to
all-zero state, the lightest error pattern reduces to all-zero, the lightest
non-zero error pattern is a valid codeword to update lightest codeword list.
Given sufficient codewords sending, the survived lightest codewords are
likely to be the target. Compared with existing techniques, our method
demonstrates its efficiency in the simulation of several interested LDPC codes.Comment: 8 pages, 1 tabl