Two-terminal source coding with common sum reconstruction

TL;DR

This paper investigates the rate-distortion limits for two terminals that aim to reconstruct the sum of correlated sources with high probability, providing bounds for a binary source case using existing coding strategies.

Contribution

It introduces inner and outer bounds for the achievable rate-distortion region in the CSR problem for binary sources, extending previous coding techniques.

Findings

Derived bounds for the rate-distortion region

Applied existing coding results to the CSR problem

Extended modulo-two sum computation techniques

Abstract

We present the problem of two-terminal source coding with Common Sum Reconstruction (CSR). Consider two terminals, each with access to one of two correlated sources. Both terminals want to reconstruct the sum of the two sources under some average distortion constraint, and the reconstructions at two terminals must be identical with high probability. In this paper, we develop inner and outer bounds to the achievable rate distortion region of the CSR problem for a doubly symmetric binary source. We employ existing achievability results for Steinberg's common reconstruction and Wyner-Ziv's source coding with side information problems, and an achievability result for the lossy version of Korner-Marton's modulo-two sum computation problem.