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Joint Source-Channel Coding for ISAC: Distortion Tradeoffs and Separation Theorems

Gefei Peng, Youlong Wu

TL;DR

The paper addresses the fundamental tradeoff among communication rate, sensing distortion, and estimation cost in ISAC by formulating a joint source-channel coding (JSCC) framework for a state-dependent SDMC. It derives an exact capacity–distortion–cost function $C_{ ext{inf}}(D_s,B)$, proves that the optimal performance is achievable via separate source and channel coding (SSCC), and establishes a separation theorem for this ISAC setting. A convexity analysis of the rate–distortion function $R(D_u,D_s)$ and a binary ISAC example validate the theoretical results, showing that the SSCC approach attains joint optimality. The findings have practical implications for ISAC system design, enabling simpler coding strategies without sacrificing fundamental performance limits, and provide insights into the interplay between sensing accuracy and communication efficiency.

Abstract

Integrated Sensing and Communication (ISAC) systems have garnered significant attention due to their capability to simultaneously achieve efficient communication and environmental sensing. A core objective in this field is characterizing the performance tradeoff between sensing and communication. In this paper, we consider a joint source-channel coding (JSCC) framework for the ISAC system that consists of a transmitter with a channel state estimator and a joint source-channel encoder, a state-dependent memoryless channel, and a receiver with a joint source-channel decoder. From an information-theoretic perspective, we establish the tradeoff relationships among channel capacity, distortions in both communication and sensing processes, and the estimation cost. We prove that the separate source and channel coding can achieve joint optimality in this setting. An illustrative example of a binary setting is also provided to validate our theoretical results.

Joint Source-Channel Coding for ISAC: Distortion Tradeoffs and Separation Theorems

TL;DR

The paper addresses the fundamental tradeoff among communication rate, sensing distortion, and estimation cost in ISAC by formulating a joint source-channel coding (JSCC) framework for a state-dependent SDMC. It derives an exact capacity–distortion–cost function , proves that the optimal performance is achievable via separate source and channel coding (SSCC), and establishes a separation theorem for this ISAC setting. A convexity analysis of the rate–distortion function and a binary ISAC example validate the theoretical results, showing that the SSCC approach attains joint optimality. The findings have practical implications for ISAC system design, enabling simpler coding strategies without sacrificing fundamental performance limits, and provide insights into the interplay between sensing accuracy and communication efficiency.

Abstract

Integrated Sensing and Communication (ISAC) systems have garnered significant attention due to their capability to simultaneously achieve efficient communication and environmental sensing. A core objective in this field is characterizing the performance tradeoff between sensing and communication. In this paper, we consider a joint source-channel coding (JSCC) framework for the ISAC system that consists of a transmitter with a channel state estimator and a joint source-channel encoder, a state-dependent memoryless channel, and a receiver with a joint source-channel decoder. From an information-theoretic perspective, we establish the tradeoff relationships among channel capacity, distortions in both communication and sensing processes, and the estimation cost. We prove that the separate source and channel coding can achieve joint optimality in this setting. An illustrative example of a binary setting is also provided to validate our theoretical results.
Paper Structure (5 sections, 6 theorems, 33 equations, 2 figures)

This paper contains 5 sections, 6 theorems, 33 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model
  3. Main Results
  4. Capacity-Distortion-Cost Tradeoff For the Binary Case
  5. Proof of Convexity of $R(D_u, D_s)$

Key Result

Lemma 1

Define the function where ties can be broken arbitrarily and Irrespective of the choice of encoding and decoding functions, distortion $\Delta_s^{(n)}$ in eq:state_dist is minimized by the estimator Notice that the function $\hat{s}^*(\cdot, \cdot)$ only depends on the SDMC channel law $P_{YZ|SX}$ and the state distribution $P_S$.

Figures (2)

  • Figure 1: The JSCC framework for the ISAC problem.
  • Figure 2: Comparison of capacity-distortion and rate-distortion for the binary channel.

Theorems & Definitions (12)

  • Definition 1
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • proof
  • Definition 2
  • Lemma 4
  • proof
  • Theorem 1
  • proof
  • ...and 2 more