On Modulo-Sum Computation over an Erasure Multiple Access Channel

TL;DR

This paper investigates the capacity of computing a modulo-sum over a two-user erasure multiple access channel, introducing new bounds and coding strategies that leverage state information and feedback.

Contribution

It presents a novel upper bound on sum-rate with partial state knowledge and demonstrates capacity improvements with causal feedback.

Findings

New upper bound on sum-rate with partial state information

Capacity increase with causal feedback

Extensions to lossy reconstruction and additional states

Abstract

We study computation of a modulo-sum of two binary source sequences over a two-user erasure multiple access channel. The channel is modeled 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 vice versa. The associated state sequence is independent and identically distributed. We develop a new upper bound on the sum-rate by revealing only part of the state sequence to the transmitters. Our coding scheme is based on the compute and forward and the decode and forward techniques. When a (strictly) causal feedback of the channel state is available to the encoders, we show that the modulo-sum capacity is increased. Extensions to the case of lossy reconstruction of the modulo-sum and to channels involving additional states are also treated briefly.