Communication Over Individual Channels

A communication problem in considered, where no mathematical model is specified for the channel. The achievable rates are determined as a function of the channel input and output sequences known a-posteriori, without assuming any a-priori relation between them. For discrete channels the empirical mutual information between the input and output sequences is shown to be achievable, while for continuous channels the achievable rate is based on the empirical correlation between the sequences. A rate-adaptive scheme employing feedback which achieves these rates asymptotically with a guaranteed reliability, without prior knowledge of the channel behavior, is presented.