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On the Rate-Exponent Region of Integrated Sensing and Communications With Variable-Length Coding

Ioannis Papoutsidakis, George C. Alexandropoulos

TL;DR

This work investigates the rate-exponent region for integrated sensing and communications (ISAC) on a Gaussian channel using variable-length feedback (VLF) codes. It derives three analytically tractable achievable regions by employing distinct input signal distributions, including Gaussian mixtures and a novel $ ext{J}(k)$-distributed input, and analyzes their error exponents for sensing under the VLF framework. The results reveal a fundamental trade-off between sensing reliability and communication rate that emerges with VLF coding, contrasting with fixed-length, constant-power ISAC settings. Numerical evaluations show that while VLF can improve non-asymptotic performance, the joint rate-exponent region can be reduced when sensing is also optimized, with time-sharing between corner points becoming favorable at high signal-to-noise ratios. The findings provide explicit, analyzable benchmarks for ISAC design under variable-length coding and feedback, and point to future work on rate-distortion considerations and generalized signaling strategies.

Abstract

This paper considers the achievable rate-exponent region of integrated sensing and communication systems in the presence of variable-length coding with feedback. This scheme is fundamentally different from earlier studies, as the coding methods that utilize feedback impose different constraints on the codewords. The focus herein is specifically on the Gaussian channel, where three achievable regions are analytically derived and numerically evaluated. In contrast to a setting without feedback, we show that a trade-off exists between the operations of sensing and communications.

On the Rate-Exponent Region of Integrated Sensing and Communications With Variable-Length Coding

TL;DR

This work investigates the rate-exponent region for integrated sensing and communications (ISAC) on a Gaussian channel using variable-length feedback (VLF) codes. It derives three analytically tractable achievable regions by employing distinct input signal distributions, including Gaussian mixtures and a novel -distributed input, and analyzes their error exponents for sensing under the VLF framework. The results reveal a fundamental trade-off between sensing reliability and communication rate that emerges with VLF coding, contrasting with fixed-length, constant-power ISAC settings. Numerical evaluations show that while VLF can improve non-asymptotic performance, the joint rate-exponent region can be reduced when sensing is also optimized, with time-sharing between corner points becoming favorable at high signal-to-noise ratios. The findings provide explicit, analyzable benchmarks for ISAC design under variable-length coding and feedback, and point to future work on rate-distortion considerations and generalized signaling strategies.

Abstract

This paper considers the achievable rate-exponent region of integrated sensing and communication systems in the presence of variable-length coding with feedback. This scheme is fundamentally different from earlier studies, as the coding methods that utilize feedback impose different constraints on the codewords. The focus herein is specifically on the Gaussian channel, where three achievable regions are analytically derived and numerically evaluated. In contrast to a setting without feedback, we show that a trade-off exists between the operations of sensing and communications.
Paper Structure (9 sections, 2 theorems, 28 equations, 2 figures)

This paper contains 9 sections, 2 theorems, 28 equations, 2 figures.

Table of Contents

  1. Introduction
  2. System Model and Analysis Objective
  3. Error Detection Probability
  4. The Rate-Exponent Region
  5. Corner Points
  6. Connecting the Corner Points: Gaussian Mixture Signals
  7. Connecting the Corner Points: A Novel Signal Distribution
  8. Numerical Results
  9. Conclusion and Future Work

Key Result

Theorem 1

For any $a\in[0,\infty)$, there exists an achievable rate-exponent tuple $(R^*,E^*)$ such that:

Figures (2)

  • Figure 1: The considered ISAC setting with feedback.
  • Figure 2: Achievable rate-exponent regions for various SNR values for the communication ($\text{SNR}_1$) and sensing ($\text{SNR}_2$) operations.

Theorems & Definitions (5)

  • Definition 1
  • Theorem 1
  • proof
  • Theorem 2
  • proof