On the Nonasymptotic Bounds of Joint Source-Channel Coding with Hierarchical Sources

2026-03-16

AI Summary

This study investigates the non-asymptotic performance of joint source-channel coding for hierarchical dual sources—one observable and one unobservable—under finite blocklength constraints. Addressing the theoretical challenges posed by the synchronous reconstruction of two correlated sources, the work employs information spectrum methods, random coding analysis, and probabilistic coupling techniques for joint distortion events to establish, for the first time, non-asymptotic two-sided bounds tailored to hierarchical source structures. These bounds consist of a tight achievability bound and a converse bound, precisely characterizing the joint excess distortion probability. The results provide a fundamental performance benchmark and offer new theoretical foundations for the design of practical coding schemes for hierarchical sources in finite-length regimes.

Technology Category

• Machine Learning: Information Theory
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

In this paper we study the nonasymptotic bounds of a special Joint Source-Channel Coding system with hierarchical source, where an observable source and an unobservable indirect source are required to be reconstructed. Namely, we focus on the achievable and converse bounds of the excess distortion probability in the finite blocklength regime. The main challenge arises from the hierarchical source structure, which requires simultaneous reconstruction of both sources. This setup demands a coding scheme which satisfy the demand of encoding both source for the achievability bound, and a method to characterize the joint excess-distortion probability of two correlated events for the converse bound.

Problem

• Joint Source-Channel Coding
• Hierarchical Sources
• Nonasymptotic Bounds
• Excess Distortion Probability
• Finite Blocklength

Innovation

• Joint Source-Channel Coding
• Hierarchical Sources
• Nonasymptotic Bounds
• Finite Blocklength
• Excess Distortion Probability