Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Covering Codes as Near-Optimal Quantizers for Distributed Testing Against Independence

Fatemeh Khaledian, Reza Asvadi, Elsa Dupraz, Tad Matsumoto

TL;DR

This investigation aims to characterize the optimal quantizer among binary linear codes, with the objective of identifying optimal error probabilities under the Neyman-Pearson (NP) criterion for short code-length regime.

Abstract

We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary linear codes, with the objective of identifying optimal error probabilities under the Neyman-Pearson (NP) criterion for short code-length regime. We define optimality as the direct minimization of analytical expressions of error probabilities using an alternating optimization (AO) algorithm. Additionally, we provide lower and upper bounds on error probabilities, leading to the derivation of error exponents applicable to large code-length regime. Numerical results are presented to demonstrate that, with the proposed algorithm, binary linear codes with an optimal covering radius perform near-optimally for the independence test in DHT.

Covering Codes as Near-Optimal Quantizers for Distributed Testing Against Independence

TL;DR

This investigation aims to characterize the optimal quantizer among binary linear codes, with the objective of identifying optimal error probabilities under the Neyman-Pearson (NP) criterion for short code-length regime.

Abstract

We explore the problem of distributed Hypothesis Testing (DHT) against independence, focusing specifically on Binary Symmetric Sources (BSS). Our investigation aims to characterize the optimal quantizer among binary linear codes, with the objective of identifying optimal error probabilities under the Neyman-Pearson (NP) criterion for short code-length regime. We define optimality as the direct minimization of analytical expressions of error probabilities using an alternating optimization (AO) algorithm. Additionally, we provide lower and upper bounds on error probabilities, leading to the derivation of error exponents applicable to large code-length regime. Numerical results are presented to demonstrate that, with the proposed algorithm, binary linear codes with an optimal covering radius perform near-optimally for the independence test in DHT.

Paper Structure

This paper contains 12 sections, 4 theorems, 32 equations, 3 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. DHT against independence for Binary Symmetric Sources
  4. Linear block codes and useful properties
  5. Analysis of Optimum Quantizer
  6. The quantizer structure under Neyman-Pearson criterion
  7. Short code-length regime
  8. Large code-length regime
  9. Numerical Results
  10. Conclusions
  11. Proof of Lemma 1
  12. Proof of Proposition 1

Key Result

Lemma 1

With the blocklength $n$ and an integer threshold $0 \textcolor{black}{\leq} \gamma_t \leq n$, Type-II error probability can be expressed as:

Figures (3)

  • Figure 1: Two-node system for distributed hypothesis testing problem.
  • Figure 2: ROC curves: exact values (solid lines), lower bounds (dash-dotted lines), and upper bounds (dashed lines).
  • Figure 3: The tradeoff between Type-I and Type-II in terms of $E_0$ and $E_1$.

Theorems & Definitions (6)

  • Definition 1: covering radius cohen1997covering
  • Definition 2: coset leader spectrum
  • Lemma 1
  • Corollary 1
  • Proposition 1
  • Corollary 2