Code construction for the ideal two-user Poisson multiple-access channel with noiseless feedback

The ideal two-user Poisson multiple-access channel (MAC) with noiseless feedback models a direct detection MAC, free of dark current, in which a causal feedback link informs both encoders at every time t of the channel output at all times prior to t. Coding for this channel, under peak power and average-power constraints on both inputs, but with unlimited bandwidth is considered. The scheme incorporates two-way communication between the encoders, backward decoding, and the notion of superposition block Markov encoding. The rate-sum attainable via this code construction improves on the inner bound.