Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Shuo Shao, Chao Qi, Jincheng Dai

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.

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

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.
Paper Structure (6 sections, 2 theorems, 5 equations, 1 figure)

This paper contains 6 sections, 2 theorems, 5 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Problem Formulation and Important Notations
  3. System Model
  4. General Converse Bounds
  5. Converse Bounds with General and Linear Relaxation Functions
  6. General Achievable Bounds and Coding scheme

Key Result

Theorem 1

For any achievable tuple of $(\mathsf{D}_s, \mathsf{D}_x, \epsilon)$, the following inequality must hold: for any $\mathsf{d}(\mathsf{d}_s,\mathsf{d}_x)$ which is monotonically non-decreasing with $\mathsf{d}_s$ and $\mathsf{d}_x$. Here the random variable tuple $(S,X,Y,Z,\hat{X},\hat{Z})$ follows a distribution

Figures (1)

  • Figure 1: A semantic-aware communication system model equipped with an $(n,k,\mathsf{D}_s,\mathsf{D}_x)$ lossy joint source-channel code

Theorems & Definitions (2)

  • Theorem 1: Converse bound with general $\mathsf{d}$($\cdot$,$\cdot$) function
  • Theorem 2