On the probability of error for communication in white Gaussian noise

Abstract

Lower bounds on the error probability are obtained for communication with average powerPand no bandwidth constraint in the presence of white Gaussian noise with spectral densityN. For ratesRless than the channel capacityC = P/N, these bounds show that the error-exponent (reliability)E(R)satisfiesE(R) \leq \left{ ^{C/2 -R, \mbox{R \leq C/4,}}_{(\sqrt{C}-\sqrt{R})^{2}, \mbox{R \geq C/4}}.Since this exponent can be achieved with orthogonal signals, the reliability is now known exactly. For rates exceeding the capacity, it is shown that the error probability approaches unity as the delay approaches infinity. This is a "strong converse" for this channel.