Source Broadcasting to the Masses: Separation has a Bounded Loss

TL;DR

This paper analyzes the source broadcasting problem, providing bounds on the loss caused by separation and time-sharing, showing that separation remains near-optimal even as the number of receivers grows, especially for degraded channels.

Contribution

It establishes bounds on the rate loss due to separation in source broadcasting, demonstrating near-optimality of separation-based schemes for degraded and AWGN broadcast channels.

Findings

Separation incurs a bounded loss in source broadcasting.

For degraded channels, separation achieves at least a fraction of the joint optimal rate.

In AWGN channels, separation is within one bit for two receivers, and within log2 T bits for T receivers.

Abstract

This work discusses the source broadcasting problem, i.e. transmitting a source to many receivers via a broadcast channel. The optimal rate-distortion region for this problem is unknown. The separation approach divides the problem into two complementary problems: source successive refinement and broadcast channel transmission. We provide bounds on the loss incorporated by applying time-sharing and separation in source broadcasting. If the broadcast channel is degraded, it turns out that separation-based time-sharing achieves at least a factor of the joint source-channel optimal rate, and this factor has a positive limit even if the number of receivers increases to infinity. For the AWGN broadcast channel a better bound is introduced, implying that all achievable joint source-channel schemes have a rate within one bit of the separation-based achievable rate region for two receivers, or within $\log_2 T$ bits for $T$ receivers.