Asymptotically Good LDPC Convolutional Codes With AWGN Channel Thresholds Close to the Shannon Limit

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Ensembles of asymptotically regular Low-Density ParityCheck (LDPC) block codes can be obtained by terminating regular LDPC Convolutional (LDPCC) codes,. The slight irregularity resulting from the termination of the convolutional codes leads to substantially better Belief Propagation (BP) decoding thresholds compared to their tail-biting version or the block codes they are constructed from. This threshold improvement is even visible as the termination factor tends to infinity and both the code rate and degree distributions approach those of the corresponding block codes. More recently, it has been proven analytically for the Binary Erasure Channel (BEC) that the BP decoding thresholds of some slightly modified LDPCC code ensembles approach the optimal Maximum A Posteriori probability (MAP) decoding thresholds of the corresponding LDPC block code ensembles.