New Second-Order Achievability Bounds for Coding with Side Information via Type Deviation Convergence

TL;DR

This paper introduces a new framework called type deviation convergence for second-order achievability bounds, significantly improving existing bounds in various network information theory problems involving side information.

Contribution

The paper presents a novel general framework for second-order achievability bounds applicable to multiple network information theory scenarios, with improved bounds for key problems.

Findings

Improved second-order bounds for Wyner-Ziv problem

Enhanced bounds for Heegard-Berger problem

Stronger results for Gelfand-Pinsker channels with cost

Abstract

We propose a framework for second-order achievability, called type deviation convergence, that is generally applicable to settings in network information theory, and is especially suitable for lossy source coding and channel coding with cost. We give a second-order achievability bound for lossy source coding with side information at the decoder (Wyner-Ziv problem) that improves upon all known bounds (e.g., Watanabe-Kuzuoka-Tan, Yassaee-Aref-Gohari and Li-Anantharam). We also give second-order achievability bounds for lossy compression where side information may be absent (Heegard-Berger problem) and channels with noncausal state information at the encoder and cost constraint (Gelfand-Pinsker problem with cost) that improve upon previous bounds.