Joint Channel-State Estimation and Decoding of Low-Density Parity-Check Codes on the Two-State Noiseless/Useless BSC Block Interference Channel

Joint Channel-State Estimation and Decoding of Low-Density Parity-Check Codes on the Two-State Noiseless/Useless BSC Block Interference Channel We apply the density-evolution technique to determine the thresholds of low-density parity-check (LDPC) codes when the sum-product algorithm is employed to perform joint channel-state estimation and decoding. The channel considered is the two-state noiseless/useless binary symmetric channel (BSC) block interference channel, where a block of consecutive symbols shares the same channel state, which is either a noiseless BSC (crossover probability 0) or a useless BSC (crossover probability 1/2). The channel state is selected independently and at random from block to block, according to a known prior distribution. The threshold of the joint channel-state estimation/decoding scheme when used over such a channel is shown to be greatly superior to that of a decoder that makes no attempt to estimate the channel state. These results are also confirmed by simulation. The maximum-likelihood performance of LDPC codes when used over this channel is investigated. Lower bounds on the error exponents of regular LDPC codes, when maximum-likelihood decoded, are shown to be close to the random coding channel-error exponent when the LDPC variable node degree is high.