BLOCK AND TRELLIS CODES FOR THE BINARY (1-D) PARTIAL-RESPONSE CHANNELWITH SIMPLE MAXIMUM-LIKELIHOOD DECODERS

We consider block and convolutional codes for improving the reliabilit y of data transmission over the binary preceded noisy (1 - D) partial response channel, We concentrate on a class of codes for which the max imum likelihood decoder, matched to the encoder, precoder, and the cha nnel has the same trellis structure as the encoder, Thus, doubling the number of states due to the channel memory is avoided. We show that t he necessary and sufficient condition to belong to this class is that all codewords be df the same parity, The Reed-Muller and Golay codes b elong to this class.