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On the Fundamental Tradeoff of Joint Communication and Quickest Change Detection with State-Independent Data Channels

Daewon Seo, Sung Hoon Lim

TL;DR

This work formally establishes a joint communication and sensing problem for the quickest change detection and provides an inner bound on the information-theoretic tradeoff between communication rate and change point detection delay in the asymptotic regime of vanishing false alarm rate.

Abstract

In this work, we take the initiative in studying the information-theoretic tradeoff between communication and quickest change detection (QCD) under an integrated sensing and communication setting. We formally establish a joint communication and sensing problem for the quickest change detection. We assume a broadcast channel with a transmitter, a communication receiver, and a QCD detector in which only the detection channel is state dependent. For the problem setting, by utilizing constant subblock-composition codes and a modified CuSum detection rule, which we call subblock CuSum (SCS), we provide an inner bound on the information-theoretic tradeoff between communication rate and change point detection delay in the asymptotic regime of vanishing false alarm rate. We further provide a partial converse that matches our inner bound for a certain class of codes. This implies that the SCS detection strategy is asymptotically optimal for our codes as the false alarm rate constraint vanishes. We also present some canonical examples of the tradeoff region for a binary channel, a scalar Gaussian channel, and a MIMO Gaussian channel.

On the Fundamental Tradeoff of Joint Communication and Quickest Change Detection with State-Independent Data Channels

TL;DR

This work formally establishes a joint communication and sensing problem for the quickest change detection and provides an inner bound on the information-theoretic tradeoff between communication rate and change point detection delay in the asymptotic regime of vanishing false alarm rate.

Abstract

In this work, we take the initiative in studying the information-theoretic tradeoff between communication and quickest change detection (QCD) under an integrated sensing and communication setting. We formally establish a joint communication and sensing problem for the quickest change detection. We assume a broadcast channel with a transmitter, a communication receiver, and a QCD detector in which only the detection channel is state dependent. For the problem setting, by utilizing constant subblock-composition codes and a modified CuSum detection rule, which we call subblock CuSum (SCS), we provide an inner bound on the information-theoretic tradeoff between communication rate and change point detection delay in the asymptotic regime of vanishing false alarm rate. We further provide a partial converse that matches our inner bound for a certain class of codes. This implies that the SCS detection strategy is asymptotically optimal for our codes as the false alarm rate constraint vanishes. We also present some canonical examples of the tradeoff region for a binary channel, a scalar Gaussian channel, and a MIMO Gaussian channel.
Paper Structure (16 sections, 8 theorems, 103 equations, 6 figures)

This paper contains 16 sections, 8 theorems, 103 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Preliminary on QCD
  3. Problem Statement
  4. Main Results
  5. Evaluation Examples
  6. Binary channels
  7. Scalar Gaussian channels
  8. Example application to passive radar detection
  9. MIMO Gaussian channels
  10. Discussions
  11. Proof of Theorem \ref{['thm:theorem1']}
  12. Coding Rate Analysis
  13. QCD Delay Analysis
  14. Proof of Theorem \ref{['thm:theorem2']}
  15. Proof of Theorem \ref{['thm:theorem3']}
  16. ...and 1 more sections

Key Result

Theorem 1

Let $\mathscr{R}_{\textsf{in}}$ be the set of rate-delay pairs $(R, \Delta) \in \mathbb{R}_+^2$ such that for some $p_X$, where $p^{(s)} := p_{Y|X,s}$. Then, $\mathscr{R}_{\textsf{in}} \subset \mathscr{R}$. In other words, any point in $\mathscr{R}_{\textsf{in}}$ is achievable.

Figures (6)

  • Figure 1: Problem model of joint communication and QCD.
  • Figure 2: The distribution of the QCD channel changes at some turning point $\nu$ from the baseline distribution $p^{(0)}$ to the abnormal distribution $p^{(1)}$.
  • Figure 3: Monostatic model for ISAC. The encoder and QCD detector are the same entity which has access to some feedback.
  • Figure 4: Channels considered in the binary example.
  • Figure 5: Plot for the binary channel example where $\epsilon = 0.3$, $\epsilon_0 = 0.1$, $\epsilon_1 = 0.5$.
  • ...and 1 more figures

Theorems & Definitions (15)

  • Definition 1: stopping rule
  • Theorem 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Corollary 1
  • Remark 4
  • Definition 2: sliding-window typical codes
  • Remark 5
  • Theorem 2
  • ...and 5 more