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 (1988) single-user codes is shown to be exponentially optimum for this case as well. Second, the sphere packing bounding technique suggested in Burnashev and Kutoyants(1999) is generalised to the case at hand and an upper bound on the error exponent, which coincides with the lower bound, is derived