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Random Gilbert-Varshamov Codes for Joint Source-Channel Coding

AmirPouya Moeini, Albert Guillén i Fàbregas

TL;DR

The paper develops a random Gilbert-Varshamov–type code construction for joint source-channel coding of discrete memoryless sources and channels. By leveraging a type-dependent, distance-based codebook with per-type distributions, it constructs an ensemble that achieves both the random-coding and expurgated error exponents in JSCC. The approach extends recursive distance-based GV coding to the JSCC setting and yields a universal, distribution-agnostic construction that matches established exponents. This strengthens the theoretical understanding of JSCC performance limits and provides a robust coding blueprint with strong error-probability guarantees.

Abstract

We propose a random coding technique for joint source-channel coding of discrete memoryless sources and channels. The approach builds on the random Gilbert-Varshamov code construction of Somekh-Baruch et al. and extends it to the joint source-channel setting. We show that the resulting ensemble attains the maximum of the random-coding and expurgated error exponents.

Random Gilbert-Varshamov Codes for Joint Source-Channel Coding

TL;DR

The paper develops a random Gilbert-Varshamov–type code construction for joint source-channel coding of discrete memoryless sources and channels. By leveraging a type-dependent, distance-based codebook with per-type distributions, it constructs an ensemble that achieves both the random-coding and expurgated error exponents in JSCC. The approach extends recursive distance-based GV coding to the JSCC setting and yields a universal, distribution-agnostic construction that matches established exponents. This strengthens the theoretical understanding of JSCC performance limits and provides a robust coding blueprint with strong error-probability guarantees.

Abstract

We propose a random coding technique for joint source-channel coding of discrete memoryless sources and channels. The approach builds on the random Gilbert-Varshamov code construction of Somekh-Baruch et al. and extends it to the joint source-channel setting. We show that the resulting ensemble attains the maximum of the random-coding and expurgated error exponents.
Paper Structure (8 sections, 3 theorems, 44 equations)

This paper contains 8 sections, 3 theorems, 44 equations.

Table of Contents

  1. Introduction
  2. Notation
  3. Preliminaries
  4. Random Codebook Generation
  5. Achievable Error Exponents
  6. Achieving the Random Coding Error Exponent
  7. Achieving the Expurgated Error Exponent
  8. Proofs

Key Result

Lemma 1

Let $\boldsymbol{v} \in \mathcal{T}^k(P_i)$. Then the marginal distribution of the corresponding codeword $\boldsymbol{X}_{\boldsymbol{v}}$ is uniform over $\mathcal{T}^n(Q_{\mu(i)})$, and zero otherwise.

Theorems & Definitions (3)

  • Lemma 1
  • Lemma 2
  • Theorem 1