  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.
