Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance

Details Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance

2010-12-07

arxiv.org/abs/1012.1425v1

Computer Science

Information Theory

17 pages, 8 figures, Submitted to IEEE Transactions on Information Theory

Scientific paper

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.

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