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Pseudo-codeword performance analysis for LDPC convolutional codes

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R. Smarandache, A. E. Pusane, P. O. Vontobel, and D. J. Costello, Jr., IEEE Transactions on Information Theory, Vol. 55, No.6, pp. 2577-2598, June 2009.

Abstract- 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.

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