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Integrated Sensing and Communication in the Finite Blocklength Regime

Homa Nikbakht, Michèle Wigger, Shlomo Shamai, H. Vincent Poor

TL;DR

This work analyzes a point-to-point ISAC system operating over a discrete memoryless state-dependent channel in the finite blocklength regime. It derives achievability and converse bounds on the rate-distortion-error tradeoff and characterizes the second-order rate-distortion-error region, using a symbolwise optimal estimator for the channel state. Numerical results on a binary channel with multiplicative Bernoulli state show that the proposed joint ISAC design significantly outperforms time-sharing baselines. The findings illuminate finite-blocklength limits for ISAC and guide practical joint design under latency-constrained scenarios.

Abstract

A point-to-point integrated sensing and communication (ISAC) system is considered where a transmitter conveys a message to a receiver over a discrete memoryless channel (DMC) and simultaneously estimates the state of the channel through the backscattered signals of the emitted waveform. We derive achievability and converse bounds on the rate-distortion-error tradeoff in the finite blocklength regime, and also characterize the second-order rate-distortion-error region for the proposed setup. Numerical analysis shows that our proposed joint ISAC scheme significantly outperforms traditional time-sharing based schemes where the available resources are split between the sensing and communication tasks.

Integrated Sensing and Communication in the Finite Blocklength Regime

TL;DR

This work analyzes a point-to-point ISAC system operating over a discrete memoryless state-dependent channel in the finite blocklength regime. It derives achievability and converse bounds on the rate-distortion-error tradeoff and characterizes the second-order rate-distortion-error region, using a symbolwise optimal estimator for the channel state. Numerical results on a binary channel with multiplicative Bernoulli state show that the proposed joint ISAC design significantly outperforms time-sharing baselines. The findings illuminate finite-blocklength limits for ISAC and guide practical joint design under latency-constrained scenarios.

Abstract

A point-to-point integrated sensing and communication (ISAC) system is considered where a transmitter conveys a message to a receiver over a discrete memoryless channel (DMC) and simultaneously estimates the state of the channel through the backscattered signals of the emitted waveform. We derive achievability and converse bounds on the rate-distortion-error tradeoff in the finite blocklength regime, and also characterize the second-order rate-distortion-error region for the proposed setup. Numerical analysis shows that our proposed joint ISAC scheme significantly outperforms traditional time-sharing based schemes where the available resources are split between the sensing and communication tasks.
Paper Structure (19 sections, 3 theorems, 22 equations, 3 figures)

This paper contains 19 sections, 3 theorems, 22 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Setup
  3. Optimal Estimator
  4. Main Results
  5. Comparisons and Examples
  6. Time-Sharing Schemes
  7. Basic Resource-Sharing Scheme
  8. Improved Resource-Sharing Scheme
  9. Binary Channel with Multiplicative Bernoulli State
  10. Numerical Analysis
  11. Proof of Theorem \ref{['th1']}
  12. Codebook Generation
  13. Encoding
  14. Estimation
  15. Decoding
  16. ...and 4 more sections

Key Result

Theorem 1

Given a blocklength $n$, the rate-distortion-error tradeoff $(\mathsf{R}, \mathsf{D}, \epsilon)$ is achievable if there exists a $P_X$ and a constant $\mathsf{K} >0$ such that the following two conditions are satisfied, with and where the mutual information $I(X;Y)$ and the two central moments $\mathsf{V}$ and $\mathsf{T}$ are defined based on the joint pmf $P_{XY}(x,y)=P_X(x)P_{Y|X}(y|x)$.

Figures (3)

  • Figure 1: ISAC System model.
  • Figure 2: Achievability and converse bounds on the rate-distortion-error trade-off of Theorems \ref{['th1']} and \ref{['th2']} for $\epsilon = 0.05$, $q = 0.4$, and different values of $n$.
  • Figure 3: Comparison of the rate-distortion-error trade-off in Theorems \ref{['th1']} and \ref{['th2']} with the basic and improved resource-sharing schemes for $\epsilon = 0.05$, $q = 0.4$, and $n = 700$.

Theorems & Definitions (5)

  • Definition 1
  • Theorem 1: Achievability Bound
  • Theorem 2: Converse Bound
  • Proposition 1
  • Remark 1