The sum-capacity of discrete-noise multiple-access channels with single-user decoding and identical codebooks

We consider an additive multiple-access channel model where all users are constrained to use identical codebooks, and where single-user decoding is performed at the receiver. We study the sum-capacity of the channel for an arbitrarily large, but finite, number of users. For a noiseless n-user channel, we construct a signaling scheme that achieves rates per user that are arbitrarily large, proving that the sum-capacity is infinite, whether the users are average and/or peak power limited or not. We show that this result still holds whenever an arbitrary discrete-noise component is added, provided there exists a positive lower bound on the separation between noise samples. Whenever the noise is of bounded support, the non power-constrained sum-capacity is also proven to be infinite. The results are valid for an asynchronous multiple-access channel with single-user decoding, as the appropriate channel model is identical to the one studied in this work.