Pseudocodeword Performance Analysis for LDPC Convolutional Codes

Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudocodewords. These failures can cause the large signal-to-noise ratio (SNR) performance of message-passing iterative decoding to be worse than that predicted by the maximum-likelihood (ML) decoding union bound. In this paper, we address the pseudocodeword problem from the convolutional code perspective. In particular, we compare the performance of LDPC convolutional codes with that of their "wrapped" quasi-cyclic block versions and we show that the minimum pseudoweight of an LDPC convolutional code is at least as large as the minimum pseudoweight of an underlying quasi-cyclic code. This result, which parallels a well-known relationship between the minimum Hamming weight of convolutional codes and the minimum Hamming weight of their quasi-cyclic counterparts, is due to the fact that every pseudocodeword in the convolutional code induces a pseudocodeword in the block code with pseudoweight no larger than that of the convolutional code\´s pseudocodeword. This difference in the weight spectra leads to improved performance at low-to-moderate SNRs for the convolutional code, a conclusion supported by simulation results.