One-Shot Broadcast Joint Source-Channel Coding with Codebook Diversity

TL;DR

This paper investigates a one-shot broadcast source-channel coding scenario, revealing that using disjoint codebooks at each decoder provides a diversity gain, and introduces coding schemes that optimize this effect.

Contribution

It introduces novel coding schemes leveraging codebook diversity in one-shot broadcast settings and derives achievability bounds using an adapted Poisson matching lemma.

Findings

Disjoint codebooks at decoders yield a diversity gain distinct from channel diversity.

Hybrid coding schemes outperform fully shared or disjoint codebook strategies.

Numerical results show improved performance on binary symmetric channels.

Abstract

We study a one-shot joint source-channel coding setting where the source is encoded once and broadcast to $K$ decoders through independent channels. Success is predicated on at least one decoder recovering the source within a maximum distortion constraint. We find that in the one-shot regime, utilizing disjoint codebooks at each decoder yields a codebook diversity gain, distinct from the channel diversity gain that may be expected when several decoders observe independent realizations of the channel's output but share the same codebook. Coding schemes are introduced that leverage this phenomenon, where first- and second-order achievability bounds are derived via an adaptation of the Poisson matching lemma which allows for multiple decoders using disjoint codebooks. We further propose a hybrid coding scheme that partitions decoders into groups to optimally balance codebook and channel diversity. Numerical results on the binary symmetric channel demonstrate that the hybrid approach outperforms strategies where the decoders' codebooks are either fully shared or disjoint.