Approximate Characterizations for the Gaussian Source Broadcast Distortion Region

TL;DR

This paper derives new outer bounds and approximate characterizations for the distortion region in Gaussian source broadcast channels with bandwidth mismatch, showing the effectiveness of source-channel separation within constant factors.

Contribution

It introduces a novel outer bound using multiple auxiliary variables and extends the results to general broadcast channels, improving understanding of achievable distortions.

Findings

Outer bounds for Gaussian source broadcast distortion region derived

Source-channel separation achieves near-optimal performance within constant factors

Results extend to general broadcast channels

Abstract

We consider the joint source-channel coding problem of sending a Gaussian source on a K-user Gaussian broadcast channel with bandwidth mismatch. A new outer bound to the achievable distortion region is derived using the technique of introducing more than one additional auxiliary random variable, which was previously used to derive sum-rate lower bound for the symmetric Gaussian multiple description problem. By combining this outer bound with the achievability result based on source-channel separation, we provide approximate characterizations of the achievable distortion region within constant multiplicative factors. Furthermore, we show that the results can be extended to general broadcast channels, and the performance of the source-channel separation based approach is also within the same constant multiplicative factors of the optimum.