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 time <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</tex> can depend on the noise at times <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\tau &lt; t</tex> and 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.