Sequential signaling over the single-user and two-user multiple-access Poisson channel subject to peak and average power constraints is considered. It is assumed that the information is transmitted in blocks, and the channel is corrupted by additive

constant dark current with rate . Furthermore, it is assumed that a noiseless delayless feedback link is employed in the communication system. It is well known that feedback does not increase the capacity of a single-user discrete memoryless channel as shown by Shannon (1967), and later generalized to continuous-time memoryless channels by Kadota (1971). However, unbounded random transmission time codes can improve significantly the attainable error exponent. In Schalkwijk and Barron (1971), a sequential signaling scheme is proposed for the single-user peak-limited and bandwidth unlimited additive white Gaussian noise channel. It improves on the reliability function of  the one-way infinite bandwidth AWGN channel Wyner (1967), and the attainable error exponent for this signaling scheme is given by

where  is the permissible peak-to-average power ratio and  is the channel capacity.

For the ideal Poisson channel Lapidoth (1993) showed that feedback improves on the fixed transmission-time error exponent and attains zero error with random transmission-time codes. In this work we analyze the performance of a sequential signaling scheme, similar to the one proposed by Schalkwijk and Barron, for the Poisson channel. In the single-user case and low power regime the error exponent is determined and it is given by . This exponent is attained with . In the two-user multiple-access case an attainable error exponent is established for the low power regime and it is given by  where  is the rate sum capacity. Again, this exponent is attained with .