On the computational cutoff rate, R(o), for the peak-power- limited Gaussian channel.

This paper starts with a brief tutorial background, which reveals the origin and the significance of R(o). Next, the problem of achieving R(o) over the additive-white-Gaussian-noise (AWGN) dispersive or nondispersive channel, using quadrature- amplitude modulation (QAM) with a peak-power constraint, is addressed. Our major result is that, for both cases, the optimum transmission signal set is chosen from a discrete distribution. The solution is derived in detail for the peak-power-limited nondispersive channel, where it is shown that the optimum QAM symbols are to be selected independently from a probability distribution that is uniform in the phase, and discrete in the radius. The solution for the corresponding peak-power- limited dispersive channel is obtained only asymptotically, for large signal-to-noise ratio (SNR), where it is shown that each QAM symbol is to be selected independently from a uniform distribution within a disc in the complex signal space.