Optimal signal sets for multiple-access channels

In a coded digital communication system, the combination of the modulator, waveform channel, and demodulator can be considered as a discrete channel for communication from the encoder to the decoder, which act to combat errors between a transmitted message and its reproduced version at the receiver. We would like to design modulation schemes which present the "best" discrete channel to the encoder and decoder, resulting in an improved performance of the overall system. This is achieved by optimizing a suitable measure of performance of the communication channel. We use the cutoff-rate region [1] of a multiple-access channel with two senders and a single receiver as a measure of performance of the communication channel. The extension to the general multiple-access channel with M senders is straighforward, and the results are similar.