B. J. Frey, R. Koetter and A. Vardy 2001.
Signal space characterization of iterative decoding.
IEEE Transactions on Information Theory 47:2, 766-781.
By tracing the flow of computations in the iterative decoders
for low density parity check codes, we are able to
formulate a signal-space view for a finite number of iterations
in a finite-length code.
On a Gaussian channel, maximum \emph{a posteriori} codeword decoding
(or ``maximum likelihood decoding'') decodes to the codeword
signal that is closest to the channel output in Euclidean distance.
In contrast, we show that iterative decoding decodes to the
``pseudosignal''
that has highest \emph{correlation} with the channel output. The set
of pseudosignals corresponds to ``pseudocodewords'', only a vanishingly
small number of which correspond to codewords.
We show that some pseudocodewords cause decoding
errors, but that there are also pseudocodewords that frequently
correct the deleterious effects of other pseudocodewords.
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