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Syndrome-based Fusion Rules in Heterogeneous Distributed Quickest Change Detection

Wen-Hsuan Li, Yu-Chih Huang

TL;DR

This work tackles heterogeneous distributed quickest change detection with 1-bit non-anonymous feedback. It introduces syndrome-based fusion rules and leverages the Hasse diagram of syndromes to derive bounds on second-order performance (EDD) as a function of ARL, while proposing pruning-based methods to design the weighted voting rule. The paper then revisits the weighted M voting rule within this framework, providing explicit design criteria via critical syndromes and an efficient pruning algorithm to select the weightings and threshold M. Simulation results demonstrate that the proposed design achieves superior second-order performance compared to anonymous and group-based rules, validating the practical impact for distributed detection in heterogeneous networks.

Abstract

In this paper, the heterogeneous distributed quickest change detection (HetDQCD) with 1-bit non-anonymous feedback is studied. The concept of syndromes is introduced and the family of syndrome-based fusion rules is proposed, which encompasses all deterministic fusion rules as special cases. Through the Hasse diagram of syndromes, upper and lower bounds on the second-order performance of expected detection delay as a function of average run length to false alarm are provided. An interesting instance, the weighted voting rule previously proposed in our prior work, is then revisited, for which an efficient pruning method for breadth-first search in the Hasse diagram is proposed to analyze the performance. This in turn assists in the design of the weight threshold in the weighted voting rule. Simulation results corroborate that our analysis is instrumental in identifying a proper design for the weighted voting rule, demonstrating consistent superiority over both the anonymous voting rule and the group selection rule in HetDQCD.

Syndrome-based Fusion Rules in Heterogeneous Distributed Quickest Change Detection

TL;DR

This work tackles heterogeneous distributed quickest change detection with 1-bit non-anonymous feedback. It introduces syndrome-based fusion rules and leverages the Hasse diagram of syndromes to derive bounds on second-order performance (EDD) as a function of ARL, while proposing pruning-based methods to design the weighted voting rule. The paper then revisits the weighted M voting rule within this framework, providing explicit design criteria via critical syndromes and an efficient pruning algorithm to select the weightings and threshold M. Simulation results demonstrate that the proposed design achieves superior second-order performance compared to anonymous and group-based rules, validating the practical impact for distributed detection in heterogeneous networks.

Abstract

In this paper, the heterogeneous distributed quickest change detection (HetDQCD) with 1-bit non-anonymous feedback is studied. The concept of syndromes is introduced and the family of syndrome-based fusion rules is proposed, which encompasses all deterministic fusion rules as special cases. Through the Hasse diagram of syndromes, upper and lower bounds on the second-order performance of expected detection delay as a function of average run length to false alarm are provided. An interesting instance, the weighted voting rule previously proposed in our prior work, is then revisited, for which an efficient pruning method for breadth-first search in the Hasse diagram is proposed to analyze the performance. This in turn assists in the design of the weight threshold in the weighted voting rule. Simulation results corroborate that our analysis is instrumental in identifying a proper design for the weighted voting rule, demonstrating consistent superiority over both the anonymous voting rule and the group selection rule in HetDQCD.
Paper Structure (13 sections, 3 theorems, 36 equations, 3 figures, 1 algorithm)

This paper contains 13 sections, 3 theorems, 36 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background
  3. Problem formulation
  4. Local CUSUM and voting rules
  5. Syndrome-based Fusion Rule
  6. Weighted $M$ Voting Rule
  7. Simulation Results
  8. Conclusions
  9. Proof of Equation \ref{['equ:2nd_ADD_mvote']}
  10. Proof of Theorem \ref{['thm:omega_fusion_rule']}
  11. Proof of Theorem \ref{['thm:weighted_voting_rule']}
  12. Proof of Fact \ref{['fact:top_low_sum']}
  13. Proof of Fact \ref{['fact:complexity_algo_pruning']}

Key Result

Theorem 1

Let $\mathbf{h} \mathnormal=[\mathcal{I}_{1}h,\cdots,\mathcal{I}_{L}h]^{T}$. Assume that And define $\lambda:[N] \rightarrow [L]$ by Then as $h \rightarrow \infty$, Only $\leq$ in equ:2nd_ADD_mvote was proved in ref:ISIT23. We extend it to equality in Appendix pf:2nd_ADD_mvote.where $\xi_{M}$ is the expected value of $M$-th order statistics of independent (but not necessarily identical) Gaussia

Figures (3)

  • Figure 1: An example of general fusion rule. Any positive feedback from $(2,1)$ or the consensus decision from group $1$ will trigger the fusion center.
  • Figure 2: (a) Second-order approximation of $E_0(\bar{\rho}_{M}( \mathbf{h},\boldsymbol{\alpha}))$ in case 1. (b) Comparison of $\bar{\rho}_{M}( \mathbf{h},\boldsymbol{\alpha})$, $\textrm{T}_{M}( \mathbf{h},\mathcal{G})$ and $\textrm{T}_{M}(\mathbf{h},\mathcal{G}_L)$ in case 1. The proposed $M$ for weighted $M$ voting rule is by (a).
  • Figure 3: (a) Second-order approximation of $E_0(\bar{\rho}_{M}( \mathbf{h},\boldsymbol{\alpha}))$ in case 2. (b) Comparison of $\bar{\rho}_{M}( \mathbf{h},\boldsymbol{\alpha})$, $\textrm{T}_{M}( \mathbf{h},\mathcal{G})$ and $\textrm{T}_{M}(\mathbf{h},\mathcal{G}_L)$ in case 2. The proposed $M$ for weighted $M$ voting rule is by (a).

Theorems & Definitions (6)

  • Theorem 1
  • Definition 1
  • Theorem 2
  • Theorem 3
  • Remark 1
  • Remark 2