On the Schalkwijk-Kailath coding scheme with a peak energy constraint

In a recent series of papers, [2]-[4] Schalkwijk and Kailath have proposed a block coding scheme for transmission over the additive white Gaussian noise channel with one-sided spectral density using a noiseless delayless feedback link. The signals have bandwidth and average power . They show how to communicate at rates , the channel capacity, with error probability (where is the coding delay), a "double exponential" decay. In their scheme the signal energy (in a -second transmission) is a random variable with only its expectation constrained to be . In this paper we consider the effect of imposing a peak energy constraint on the transmitter such that whenever the Schalkwijk-Kailath scheme requires energy exceeding a (where is a fixed parameter) transmission stops and an error is declared. We show that the error probability is degraded to a "single exponential" form and find the exponent . In the case . For finite is given by a more complicated expression.