On Survivor Error Patterns For Maximum Likelihood Soft Decoding
Jakov Snyders · 2005
Summary Consider an (t1.k.d) binary linear block code specified by a parity-check matrix H. Assume that codewords with equal proba- bility are transmitted through a niemoryless channel. Let Y be the bit-by-bit hard-detected version of the received word, and assume that z, the corresponding syndrome, is nonzero. A set of 1 linearly independent columns of H that adds up to z will be called a /-pat- tern. Thus t does not exceed ni where n1 = ti-k is the number of check bits. A palier'ri is a I-pattern with unspecified 1. Assume, without essential loss of generality, that d t 3. Let r be the set of columns of H; then IF( = ri due to the aforementioned assumption. The ivei,oh/ of a column h of H is defined to be the confidence value (magnitude of the log likelihood ratio) of the bit associated with h. The weigh/ of a subset @ of r is the sum of the weights of the elements of @. An algorithm (I) for carrying out maximum likelihood decoding may now be phrased as follows: I) among all the /-patterns, with 1 ranging up to ni, find (the usually unique) one with least weight, then