On the probability of error for communication in white Gaussian noise

Lower bounds on the error probability are obtained for communication with average power
P
and no bandwidth constraint in the presence of white Gaussian noise with spectral density
N
. For rates
R
less than the channel capacity
C = P/N
, these bounds show that the error-exponent (reliability)
E(R)
satisfies
E(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.