[论文解读] Random Gilbert-Varshamov Codes for Joint Source-Channel Coding

AmirPouya Moeini, Albert Guillén i Fàbregas|arXiv (Cornell University)|Jan 21, 2026

Wireless Communication Security Techniques被引用 0

一句话总结

The paper introduces a random coding JSCC scheme based on Gilbert-Varshamov-type constructions that achieves the maximum of the random-coding and expurgated exponents for discrete memoryless sources and channels.

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.

研究动机与目标

• Develop a random coding framework for joint source-channel coding (JSCC) of discrete memoryless sources and channels.
• Extend the recursive distance-based Gilbert-Varshamov code construction to the JSCC setting.
• Show that the resulting code ensemble attains the maximum of the random-coding and expurgated error exponents.
• Provide a universal code construction whose performance does not depend on source or channel distributions.

提出的方法

• Define a type-dependent distance function and a collection of codeword distributions partitioned by source type.
• Generate codebooks recursively to ensure minimum-distance constraints within and across source-type classes.
• Use a type-dependent decoding metric to analyze error exponents.
• Set distance parameters and decoding rules to recover random-coding and expurgated JSCC exponents.
• Employ Csiszár’s generalized mutual information and expurgated bounds to derive the exponents.
• Prove that the ensemble achieves both the random-coding and expurgated exponents under appropriate choices.

实验结果

研究问题

• RQ1 Can a random Gilbert-Varshamov-type code ensemble be extended to joint source-channel coding while preserving optimal error exponents?
• RQ2 What distance constraints and decoding metrics yield the maximum of random-coding and expurgated exponents in JSCC?
• RQ3 Is the resulting JSCC ensemble universal with respect to source and channel distributions?

主要发现

• The proposed ensemble achieves the maximum of the random-coding and expurgated exponents for JSCC.
• With appropriate distance choices (d(P) = -I(P)) and minimum-distance shifts, the construction remains universal and non-distribution-specific.
• The random-coding exponent bound matches the JSCC random-coding bound via a generalized MI decoding metric.
• The expurgated exponent bound is recovered using a specific decoding metric, yielding the Csiszár-style expurgated JSCC exponent.
• The analysis extends prior random coding constructions to joint source-channel settings, providing rigorous achievability results.