Sequential signaling under peak-power constraint in the Poisson regime

A coding scheme for the infinite bandwidth additive white Gaussian noise (AWGN) channel with noiseless feedback has been considered in (J. P. M. Schalkwijk et al, IEEE Trans. Inform. Theory, vol. IT-17, no. 3, pp.278-282. 1971). Specifically, the authors describe a peak-power constrained sequential signalling scheme that improves the one-way coding error exponent using a causal noiseless feedback link, and a reliability function is derived for this. Based on the above, this paper investigates random transmission time schemes of the Schalkwijk-Barron type, which satisfy the peak and average power constraints (A.σA) while improving the one-way coding error exponent of the (single-user and two-user) Poissin channel when λ₀≠0. Specifically, we consider coding schemes which meet peak and average power constraints.