We examine LDPC codes decoded using linear programming (LP). Fourcontributions to the LP framework are presented. First, a new method oftightening the LP relaxation, and thus improving the LP decoder, is proposed.Second, we present an algorithm which calculates a lower bound on the minimumdistance of a specific code. This algorithm exhibits complexity which scalesquadratically with the block length. Third, we propose a method to obtain atight lower bound on the fractional distance, also with quadratic complexity,and thus less than previously-existing methods. Finally, we show how thefundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes canbe obtained.
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