Coding for a multiple-access channel

Abstract

The channel considered here is a real-number adder. Attention is restricted to the case of two sources using binary signals; hence the channel has a ternary output. The paper treats both the noiseless and noisy situations. For the noiseless case the following results are obtained: several code-construction techniques are presented; a Gilbert-like lower bound is derived; an upper bound which shows linear codes to be markedly inferior to nonlinear codes on this channel is derived. It has previously been shown that, subject to certain constraints, the capacity of this channel using multiple-access signaling is 50% greater than the capacity if the users time-share the channel. The present results show that about half of this increase is achievable with simply implemented coding techniques. For the noisy adder channel we obtain the following results: partial upper bounds on the achievable rate region are derived; codes are constructed by concatenating single-user codes and the codes are constructed for the noiseless channel; the minimum distance of these codes is lower bounded; three decoding procedures are analyzed. These results show how independent additive errors affect the code rates achievable on this channel.