Binary communication over the Gaussian channel using feedback with a peak energy constraint

Abstract

We consider binary communication over the additive white Gaussian noise channel with no bandwidth constraint on the channel input signals, assuming the availability of a noiseless delayless feedback link. Although the signals at timetcan depend on the noise at times\tau < tand are therefore random functions, we require that the signal energy never exceed a fixed level. We show that the optimal probability of error is attainable without the use of the feedback channel by using antipodal signals.