Signal-space characterization of iterative decoding

By tracing the flow of computations in the iterative decoders for low-densi ty 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 po steriori (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 "pseu dosignal" that has highest correlation with the channel output. The set of pseudosignals corresponds to "pseudocodewords," only a vanishingly small nu mber of which correspond to codewords, We show that some pseudocodewords ca use decoding errors, but that there are also pseudocodewords that frequentl y correct the deleterious effects of other pseudocodewords.