Limitations of the capacity of the M-user binary adder channel due to physical considerations

The capacity of the M-user binary adder channel, subjected to various restrictions of physical nature, is investigated. The underlying propagation media considered are (i) fiber-optic, with lossless coupling and Poisson statistics, (ii) radio, under Rayleigh fading, and (iii) radio with constant amplitudes and random phases. Whereas the capacity of the unrestricted (ideal) model for the binary adder channel is known to increase without limit with the number of users, it is shown in the present paper that, for each of these cases, the total capacity is upper-bounded by a constant independent of the number of users: in case (i) by 1.7Q_T bits per channel use, where Q_T is the parameter of the Poisson process, in case (ii) by 4.33 bits per channel use, and in case (iii) by 4.27 bits per channel use