Encoding and decoding for the minimization of message symbol error rates in linear block codes

Given any fixed linear block code, the error rates for the message symbols depend both on the encoding function and on the decoding map. This research shows how to optimize the choice of a generator matrix and decoding map simultaneously to minimize the error rates for all message symbols. The model used assumes that the distribution of messages is flat and that the distribution of error vectors defining the channel is independent of the message transmitted. In addition, it is shown that, with proper choice of coset leaders, standard array decoding is optimal in this circumstance. The results generalize previously known results on unequal error protection and are sufficiently general to apply when a code is used for error detection only.