MAXIMIN PERFORMANCE OF BINARY-INPUT CHANNELS WITH UNCERTAIN NOISE DISTRIBUTIONS

We consider uncertainty classes of noise distributions defined by a bo und on the divergence with respect to a nominal noise distribution. Th e noise that maximizes the minimum error probability for binary-input channels is found. The effect of the reduction in uncertainty brought about by knowledge of the signal-to-noise ratio is also studied. The p articular class of Gaussian nominal distributions provides an analysis tool for near-Gaussian channels. Asymptotic behavior of the least fav orable noise distribution and resulting error probability are studied in a variety of scenarios, namely: asymptotically small divergence wit h and without power constraint; asymptotically large divergence with a nd without power constraint; and asymptotically large signal-to-noise ratio.