Efficient methods for bounding the fractional distance of LDPC codes and obtaining fundamental polytopes of nonbinary and generalized codes

Abstract

A method which obtains a tight lower bound on the fractional distance of LDPC codes is proposed. This algorithm exhibits complexity which scales quadratically with the block length, and thus less than currently-known methods. We also show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained.