Minimum distance and pseudodistance lower bounds for generalised LDPC codes

Abstract: Two different ways of obtaining generalized low-density parity-check codes are considered. Lower bounds on the minimum distance, stopping distance, and pseudodistance are derived for these codes using graph based analysis. These bounds are generalizations of Tanner’s bit-oriented and parity-oriented bound for simple LDPC codes. The new bounds are useful in predicting the performance of generalized LDPC codes under maximum-likelihood decoding, graphbased iterative decoding, and linear programming decoding, and rely on the connectivity of the Tanner graph.