Upper bound on error exponent of regular LDPC codes transmitted over the BEC
IEEE Transactions on Information Theory
Bounds on threshold of regular random k-SAT
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
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In this correspondence, we estimate the variance of weight and stopping set distribution of regular low-density parity-check (LDPC) ensembles. Using this estimate and the second moment method we obtain bounds on the probability that a randomly chosen code from regular LDPC ensemble has its weight distribution and stopping set distribution close to respective ensemble averages. We are able to show that a large fraction of total number of codes have their weight and stopping set distribution close to the average