On modulo-sum computation over an erasure multiple access channel

We study computation of a modulo-sum of two binary source sequences over a two-user erasure multiple access channel. Each sender observes an independent and equiprobable binary sequence and the receiver is interested in computing the modulo-sum of these two sequences. The channel is modelled as a binary-input, erasure multiple access channel, which can be in one of three states — either the channel output is a modulo-sum of the two input symbols, or the channel output equals the input symbol on the first link and an erasure on the second link, or it equals the input symbol on the second link and an erasure on the first link. The associated state sequence is independent and identically distributed. We establish upper and lower bounds on the modulo-sum capacity. Our coding scheme uses either the compute-and-forward or the decode-and-forward techniques. The upper bound is obtained by a genie aided argument that reduces the setup to a compound multiple-access channel. It is in general is tighter than a simple upper bound obtained by revealing one of the messages to the decoders. We also briefly consider the case when a strictly causal state feedback is available to the encoders and establish that such feedback can increase the modulo-sum capacity.