This invention is concerned with an in place decoder using ordered symbol reliabilities which provides improvements in both performance and implementation of decoders for (n,k) linear, block, error correcting codes. For relatively short codeword lengths (1000 symbols) the combination of powerful codes and the ordered symbol reliabilities decoder can produce a codeword decoder error rate (Frame Error Rate, FER) better than most known decoding arrangements including iterative decoders. The decoder is an in place decoder which reduces implementation complexity. In its operation the decoder considers the least reliable symbols (for each received vector) as erasures and derives parity check equations in order to solve for these least reliable symbols. This procedure ensures that any parity check derivation failure is confined to the more reliable symbols thereby outperforming alternative methods. The decoder takes into account the possibility of errors in the symbols not considered as erasures and applies hypothetical error patterns to these symbols in order corresponding to the probability of these error patterns. In this way the decoder has a minimum FER for a given number of evaluated codewords. It is shown that the hypothetical error patterns may be determined from the sign of the partial cross correlation products between the received vector and evaluated codewords. Output codeword selection is based upon minimum squared Euclidean distance between evaluated codewords and the received vector. It is shown that extrinsic information maybe used in the symbol reliability ordering to reduce the required number of evaluated codewords for a given FER. Additionally it is shown that fast decoding may be realised by carrying out decoding after k or more symbols have been received, considering the symbols yet to be received as erased symbols.
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