Exponential error bounds for coding through noisy channels with inaccurately known statistics and for generalized decision rules

Generalized decoding decision rules provide added flexibility in a decoding scheme, and some advantages. In a generalized decoding decision rule, the following possibilities are considered: (1) the decoder has the option of not deciding at all, or rejecting all estimates. This is termed an erasure; (2) the decoder has the option of putting out more than one estimate. The resulting output is called a list. Only if the correct codeword is not on the list is there a list error. Taking into account the lack of exact knowledge of the channel statistics and assuming a mismatch between the true channel transition probabilities and the nominal probabilities used in the decoding metric, error bounds are developed for generalized decision rules. Conditions under which the error probabilities converge to zero exponentially with the block length, in spite of the presence of mismatch, are established