Message-passing iterative decoders for low-density parity-check (LDPC) block codes are known to be subject to decoding failures due to so-called pseudo-codewords. These failures can cause the large signal-to-noise ratio performance of message-passing iterative decoding to be worse than that predicted by the maximum-likelihood decoding union bound.In this paper we address the pseudo-codeword 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 pseudo-weight of an LDPC convolutional code is at least as large as the minimum pseudo-weight 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 pseudo-codeword in the convolutional code induces a pseudo-codeword in the block code with pseudo-weight no larger than that of the convolutional code's pseudo-codeword. This difference in the weight spectra leads to improved performance at low-to-moderate signal-to-noise ratios for the convolutional code, a conclusion supported by simulation results.
In this paper asymptotic methods are used to form lower bounds on the free distance to constraint length ratio of several ensembles of regular, asymptotically good, protographbased LDPC convolutional codes. In particular, we show that the free distance to constraint length ratio of the regular LDPC convolutional codes exceeds that of the minimum distance to block length ratio of the corresponding LDPC block codes.
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