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

Joseph Rowan, Buu Phan, Ashish Khisti

TL;DR

This paper addresses one-shot broadcast JSCC with $K$ decoders, where success requires at least one decoder to meet distortion $D$. It introduces the concept of codebook diversity by enforcing disjoint codebooks across decoders and develops a List Poisson Matching Lemma to derive achievability bounds, including side-information scenarios via Wyner-Ziv. A hybrid scheme balances codebook and channel diversity by grouping decoders, with second-order analyses showing a finite-blocklength advantage that scales roughly with $ frac{ ext{log}K}{n}$ in some regimes; numerical results on the BSC confirm that hybrids outperform fully shared or fully disjoint configurations. The work provides a rigorous framework for understanding diversity mechanisms in one-shot broadcast JSCC and offers practical guidance for designing multi-decoder systems in distributed sensing and related applications.

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 (Li and Anantharam, 2021) 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.

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

TL;DR

This paper addresses one-shot broadcast JSCC with decoders, where success requires at least one decoder to meet distortion . It introduces the concept of codebook diversity by enforcing disjoint codebooks across decoders and develops a List Poisson Matching Lemma to derive achievability bounds, including side-information scenarios via Wyner-Ziv. A hybrid scheme balances codebook and channel diversity by grouping decoders, with second-order analyses showing a finite-blocklength advantage that scales roughly with in some regimes; numerical results on the BSC confirm that hybrids outperform fully shared or fully disjoint configurations. The work provides a rigorous framework for understanding diversity mechanisms in one-shot broadcast JSCC and offers practical guidance for designing multi-decoder systems in distributed sensing and related applications.

Abstract

We study a one-shot joint source-channel coding setting where the source is encoded once and broadcast to 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 (Li and Anantharam, 2021) 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.
Paper Structure (18 sections, 9 theorems, 4 equations, 2 figures)

This paper contains 18 sections, 9 theorems, 4 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Main Results
  4. One-Shot Achievability with Disjoint Codebooks
  5. Second-Order Analysis
  6. Specialization to Near-Lossless JSCC
  7. Baseline Coding Scheme and Analysis
  8. Hybrid Strategy
  9. List Poisson Matching Lemma
  10. Proof of \ref{['thm:oneshot_jscc']}
  11. Proof of \ref{['thm:oneshot_jscc_wz']}
  12. Numerical Example
  13. Conclusion
  14. Proof of \ref{['lemma:clml']}
  15. Proof of \ref{['lemma:cclml']}
  16. ...and 3 more sections

Key Result

Theorem 1

Fix $P_X$ and $P_Z$. Then, with $P_W$ being the source distribution and $P_{Y \mid X}$ the channel, there exists a code for $K$ decoders with error probability satisfying where $\mathcal{B}_D(w) = \{ z \in \mathcal{Z} : d(w, z) \leq D \}$ is the permissible distortion ball and $(W, X, Y) \sim P_W \times P_X P_{Y \mid X}$.

Figures (2)

  • Figure 1: System model for broadcast JSCC with side information. The source $W$ is encoded to $X$. Decoder $k$ uses the channel output $Y_k$ and side information $T_k$ to produce its reconstruction $\hat{Z}^{(k)}$.
  • Figure 2: Comparison of achievable rates with $K$ decoders for a BSC with crossover probability $\delta = 0.05$, error tolerance $\varepsilon = 10^{-2}$ and $n \in \{10, 20\}$. The disjoint (DJ), baseline (BL) and hybrid (HY) schemes are shown.

Theorems & Definitions (9)

  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Corollary 1
  • Theorem 4
  • Lemma 1: List PML
  • Lemma 2: Conditional list PML
  • Lemma 3
  • Lemma 4: kostina2012