Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance
arXiv:1012.1425 · doi:10.1109/TIT.2011.2162224
Abstract
We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an algorithm which calculates a lower bound on the minimum distance of a specific code. This algorithm exhibits complexity which scales quadratically with the block length. Third, we propose a method to obtain a tight lower bound on the fractional distance, also with quadratic complexity, and thus less than previously-existing methods. Finally, we show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained.
17 pages, 8 figures, Submitted to IEEE Transactions on Information Theory