Channel capacity for a given decoding metric

We address the rate of transmission which is attainable on a given channel when the decoding rule is specified, perhaps suboptimally. We concentrate on decoders, termed d-decoders, which accept the codeword x “closest” to the received sequence y in the sense of a metric d(x,y), defined for sequences as an additive extension of a single-letter metric. The class of d-decoders affords many interesting problems, some of which appear to be very hard; indeed, the important graph-theoretical concepts of Shannon capacity and Sperner capacity are special cases of d-capacity