Pseudo-Codeword Performance Analysis for LDPC Convolutional Codes
<|reference_start|>Pseudo-Codeword 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 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.<|reference_end|>
@article{smarandache2006pseudo-codeword,
    title={Pseudo-Codeword Performance Analysis for LDPC Convolutional Codes},
    author={Roxana Smarandache, Ali E. Pusane, Pascal O. Vontobel, Daniel J.
  Costello Jr},
    journal={arXiv preprint arXiv:cs/0609148},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0609148},
    primaryClass={cs.IT math.IT}
}