Universally optimum block codes and convolutional codes with maximum likelihood decoding

A new proof is presented for the existence of block codes whose error probability under maximum likelihood decoding is bounded asymptotically by the random coding bound universally over all discrete memoryless channels. On the basis of this result, the existence of convolutional codes with universally optimum performance is shown. Furthermore the existence of block codes which attain the expurgated bound universally over all discrete memoryless channels is proved under the use of maximum likelihood decoding.