Minimax robust coding for channels with uncertainty statistics

The problem of minimax robust coding for classes of channels with uncertainty in their statistical description is addressed. Specific consideration is given to: (1) discrete memoryless channels with uncertainty in the probability transition matrices; (2) discrete-time stationary Gaussian channels with spectral uncertainty; and to uncertainty with classes determined by 2-alternating Choquet capacities. Both block codes and convolutional codes are considered. A robust maximum-likelihood decoding rule is derived; the rule guarantees that, for all channels in the uncertainty class and all rates smaller than a critical rate, the average probability of decoding error for the ensemble of random block codes and the ensemble of random time-varying convolutional codes converges to zero exponentially with increasing block length or constraint length, respectively. The channel capacity and cut-off rate of the class are then evaluated.