Error exponents for the two-user Poisson multiple-access channel

The error exponent of the two-user Poisson multiple-access channel under peak and average power constraints, but unlimited in bandwidth, is considered. First, a random coding lower bound on the error exponent is obtained, and an extension of Wyner's (1988) single-user codes is shown to be exponentially optimum for this case as well. Second, the sphere-packing bounding technique suggested by Burnashev and Kutoyants (see Probl. Inform. Transm., vol.35, no.2, p.3-22, 1999) is generalized to the case at hand and an upper bound on the error exponent, which coincides with the lower bound, is derived. Thus, this channel joins its single-user partner as one of very few for which the reliability function is known.