Hard-Decision Performance of LDPC Codes on Binary Symmetric Channels with Small Crossover Probabilities

Upper and lower bounds are derived on the frame error rate (FER) of low-density parity-check (LDPC) codes decoded by hard-decision iterative algorithms over binary symmetric channels (BSC). The bounds, which are tight for sufficiently small crossover probabilities of the channel, provide a good estimate of FER in this region. The derivation of the bounds is based on the enumeration of low-weight error patterns at the input of the decoder and is much less complex than the conventional Monte Carlo simulation in the crossover probability range of interest. The proposed method can be applied to any LDPC code and for any decoding algorithm