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 single-user codes [1] is shown to be exponentially optimum for this case as well. Second, the sphere packing bounding technique suggested in [2] is generalized to the case at hand and an upper bound on the error exponent, which coincides with the lower bound, is derived.