Zero-Error Sum Modulo Two with a Common Observation

TL;DR

This paper studies a source coding problem where two transmitters with shared observations aim to compute the XOR of their sources without error, establishing new bounds on the required sum-rate under Markov chain conditions.

Contribution

It introduces a novel lower bound on the sum-rate for zero-error modulo two sum computation with common observations, using a coupling argument.

Findings

New lower bound on sum-rate for the problem

Applicable when sources form a Markov chain

Enhances understanding of zero-error source coding

Abstract

This paper investigates the classical modulo two sum problem in source coding, but with a common observation: a transmitter observes $(X,Z)$, the other transmitter observes $(Y,Z)$, and the receiver wants to compute $X \oplus Y$ without error. Through a coupling argument, this paper establishes a new lower bound on the sum-rate when $X-Z-Y$ forms a Markov chain.