Two-way source coding with a helper

TL;DR

This paper characterizes the achievable rate-distortion region in a two-way source coding problem with a helper, highlighting the use of binning schemes similar to Wyner-Ziv for optimal performance.

Contribution

It provides a new characterization of the rate-distortion region with a helper in two-way coding, including explicit results for Gaussian sources and analysis of message rate trade-offs.

Findings

Helper can use binning schemes for optimal rate-distortion performance

Explicit regions derived for Gaussian sources with squared error distortion

Trade-off analysis between helper's message rate and source rate

Abstract

Consider the two-way rate-distortion problem in which a helper sends a common limited-rate message to both users based on side information at its disposal. We characterize the region of achievable rates and distortions where a Markov form (Helper)-(User 1)-(User 2) holds. The main insight of the result is that in order to achieve the optimal rate, the helper may use a binning scheme, as in Wyner-Ziv, where the side information at the decoder is the "further" user, namely, User 2. We derive these regions explicitly for the Gaussian sources with square error distortion, analyze a trade-off between the rate from the helper and the rate from the source, and examine a special case where the helper has the freedom to send different messages, at different rates, to the encoder and the decoder.