Signal-space characterization of iterative decoding
Frey, B.J.
Koetter, R.
Vardy, A.
Fac. of Comput. Sci., Waterloo Univ., Ont.;
This paper appears in: Information Theory, IEEE Transactions on
Publication Date: Feb 2001
Volume: 47,
Issue: 2
On page(s): 766-781
ISSN: 0018-9448
References Cited: 33
CODEN: IETTAW
INSPEC Accession Number: 6883287
Digital Object Identifier: 10.1109/18.910587
Current Version Published: 2002-08-07
Abstract
By tracing the flow of computations in the iterative decoders for
low-density parity-check codes, we formulate a signal-space view for a
finite number of iterations in a finite-length code. On a Gaussian
channel, maximum a posteriori (MAP) 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 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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