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Lossy Source Coding with Broadcast Side Information

Yiqi Chen, Holger Boche, Marc Geitz

TL;DR

This work analyzes lossy source coding with broadcast side information where a helper observing a correlated source communicates over a degraded broadcast channel to two receivers. It develops outer and inner bounds for the rate-distortion-bandwidth region and provides separation-based inner bounds with explicit auxiliary-variable characterizations, including special cases where the separation scheme is optimal. A Gaussian example with ρ=1 contrasts the separation-based approach against uncoded schemes, identifying regimes where each strategy is advantageous and deriving corresponding rate-distortion expressions. The results illuminate when joint source-channel coding with a helper is necessary versus when a separation-based approach suffices, with implications for multi-user JSCC design under broadcast constraints. Overall, the paper extends existing single-receiver and degraded-side-information results to a two-receiver broadcast setting with a helper, offering both general outer bounds and tractable special cases, including a detailed quadratic Gaussian analysis.

Abstract

This paper considers the source coding problem with broadcast side information. The side information is sent to two receivers through a noisy broadcast channel. We provide an outer bound of the rate--distortion--bandwidth (RDB) quadruples and achievable RDB quadruples when the helper uses a separation-based scheme. Some special cases with full characterization are also provided. We then compare the separation-based scheme with the uncoded scheme in the quadratic Gaussian case.

Lossy Source Coding with Broadcast Side Information

TL;DR

This work analyzes lossy source coding with broadcast side information where a helper observing a correlated source communicates over a degraded broadcast channel to two receivers. It develops outer and inner bounds for the rate-distortion-bandwidth region and provides separation-based inner bounds with explicit auxiliary-variable characterizations, including special cases where the separation scheme is optimal. A Gaussian example with ρ=1 contrasts the separation-based approach against uncoded schemes, identifying regimes where each strategy is advantageous and deriving corresponding rate-distortion expressions. The results illuminate when joint source-channel coding with a helper is necessary versus when a separation-based approach suffices, with implications for multi-user JSCC design under broadcast constraints. Overall, the paper extends existing single-receiver and degraded-side-information results to a two-receiver broadcast setting with a helper, offering both general outer bounds and tractable special cases, including a detailed quadratic Gaussian analysis.

Abstract

This paper considers the source coding problem with broadcast side information. The side information is sent to two receivers through a noisy broadcast channel. We provide an outer bound of the rate--distortion--bandwidth (RDB) quadruples and achievable RDB quadruples when the helper uses a separation-based scheme. Some special cases with full characterization are also provided. We then compare the separation-based scheme with the uncoded scheme in the quadratic Gaussian case.
Paper Structure (9 sections, 6 theorems, 44 equations, 2 figures)

This paper contains 9 sections, 6 theorems, 44 equations, 2 figures.

Table of Contents

  1. Introduction
  2. definitions
  3. main results
  4. Quadratic Gaussian Case when $\rho=1$
  5. proof of Theorem \ref{['coro: general outer bound degraded case']}
  6. proof of corollary \ref{['coro: T=S separation based scheme optimal case']}
  7. proof of corollary \ref{['coro: one helper deterministic distortion capacity region']}
  8. One-Receiver case
  9. achievability of corollary \ref{['coro: T=S separation based scheme optimal case']}

Key Result

Theorem 1

Given a joint distribution $P_{ST}$, for the lossy compression of the source $S$ with a helper who observes $T$ and communicates to the receiver through a degraded BC $P_{YZ|X},$ a quadruple $(R,D_1,D_2,\rho)$ is achievable only if for every distribution $P_{U|T}$, there exists a distribution $P_{\h

Figures (2)

  • Figure 1: Lossy compression with broadcasted side information
  • Figure 2: Comparison between the uncoded scheme and the separation-based scheme for different values of $D_1$ when $\sigma_s^2=1,\sigma_1^2=0.6,\sigma_2^2=0.3$.

Theorems & Definitions (16)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Theorem 1
  • Remark 1
  • Definition 5
  • Theorem 2
  • Corollary 1
  • Definition 6
  • ...and 6 more