[Paper Review] Distortion Bounds for Source Broadcast Problems

Lei Yu, Houqiang Li+1 more|arXiv (Cornell University)|Jan 21, 2016

Wireless Communication Security Techniques26 references3 citations

TL;DR

This paper establishes new inner and outer bounds on the distortion region for joint source-channel coding over memoryless broadcast channels, using a novel 'remote channels' method to derive tighter outer bounds. It generalizes and unifies existing results, recovering and extending the best-known bounds for Gaussian and binary source broadcast, including in the Wyner-Ziv setting with side information.

ABSTRACT

This paper investigates the joint source-channel coding problem of sending a memoryless source over a memoryless broadcast channel. An inner bound and several outer bounds on the admissible distortion region are derived, which respectively generalize and unify several existing bounds. As a consequence, we also obtain an inner bound and an outer bound for the degraded broadcast channel case. When specialized to the Gaussian or binary source broadcast, the inner bound and outer bound not only recover the best known inner bound and outer bound in the literature, but also generate some new results. Besides, we also extend the inner bound and outer bounds to the Wyner-Ziv source broadcast problem, i.e., source broadcast with side information available at decoders. Some new bounds are obtained when specialized to the Wyner-Ziv Gaussian and Wyner-Ziv binary cases.

Motivation & Objective

• To derive tighter inner and outer bounds on the admissible distortion region for joint source-channel coding over K-user memoryless broadcast channels.
• To generalize and unify existing bounds in the literature, particularly for Gaussian and binary sources.
• To extend the framework to the Wyner-Ziv setting where decoders have side information correlated with the source.
• To introduce a novel outer bound technique based on remote channels, differing from the conventional genie-aided method.
• To recover and improve upon the best-known performance bounds for Gaussian and binary source broadcast problems.

Proposed method

• Proposes a unified hybrid coding framework inspired by Minero et al. to derive an inner bound on the distortion region.
• Introduces a new outer bound technique by constructing a degraded (weaker) version of the original network using remote channels at receiver sides.
• Contrasts this with the genie-aided method by creating a 'weaker' network rather than a 'stronger' one, enabling tighter outer bounds.
• Applies the method to both standard and Wyner-Ziv source broadcast problems, incorporating side information at decoders.
• Uses multivariate covering and packing arguments to derive bounds, with auxiliary random variables and functions mapping to estimates.
• Specializes the bounds to Gaussian and binary sources, leveraging differential entropy and mutual information game results for Gaussian noise.

Experimental results

Research questions

• RQ1 Can a unified framework be developed to derive tighter inner and outer bounds for joint source-channel coding over K-user broadcast channels?
• RQ2 How does the proposed remote channels method improve upon existing genie-aided outer bound techniques in terms of tightness and generality?
• RQ3 To what extent can the derived bounds recover or improve upon the best-known results for Gaussian and binary source broadcast?
• RQ4 What are the implications of the framework when extended to the Wyner-Ziv setting with side information at decoders?
• RQ5 Can the bounds be used to derive new performance limits for bandwidth-mismatched source broadcast systems?

Key findings

• The proposed inner bound recovers the best-known performance for hybrid digital-analog (HDA) coding in Gaussian and binary source broadcast settings.
• The outer bound recovers the tightest known outer bounds for Gaussian and binary sources, including those by Tian et al. and Khezeli et al.
• For the Wyner-Ziv Gaussian and binary broadcast cases, the framework generates new, tighter outer bounds that improve upon the single-user cut-set bound.
• The remote channels method produces a strictly weaker network than the original, enabling a novel and tighter outer bound derivation compared to genie-aided methods.
• The bounds are general and unifying, subsuming and extending multiple existing results in the literature on joint source-channel coding.
• The framework is applicable to both standard and Wyner-Ziv source broadcast, with explicit bounds derived for bandwidth-mismatched scenarios.