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Practical Short-Length Coding Schemes for Binary Distributed Hypothesis Testing

Elsa Dupraz, Ismaila Salihou Adamou, Reza Asvadi, Tad Matsumoto

TL;DR

The paper tackles practical short-length distributed hypothesis testing (DHT) for binary sources, where theory traditionally focuses on asymptotics. It proposes three schemes built from short binary linear block codes: a truncation baseline, a binary quantizer, and a quantize-binning approach, each accompanied by exact analytical expressions for Type-I and Type-II error probabilities. Numerical results and Monte Carlo simulations show that the practical schemes, especially the quantization and quantize-binning approaches, outperform the truncation baseline and align closely with the predicted error probabilities. The work provides actionable design insights for implementing DHT in short-length regimes and outlines avenues for extending the schemes to larger lengths via interleaving and complexity reduction.

Abstract

This paper investigates practical coding schemes for Distributed Hypothesis Testing (DHT). While the literature has extensively analyzed the information-theoretic performance of DHT and established bounds on Type-II error exponents through quantize and quantize-binning achievability schemes, the practical implementation of DHT coding schemes has not yet been investigated. Therefore, this paper introduces practical implementations of quantizers and quantize-binning schemes for DHT, leveraging short-length binary linear block codes. Furthermore, it provides exact analytical expressions for Type-I and Type-II error probabilities associated with each proposed coding scheme. Numerical results show the accuracy of the proposed analytical error probability expressions, and enable to compare the performance of the proposed schemes.

Practical Short-Length Coding Schemes for Binary Distributed Hypothesis Testing

TL;DR

The paper tackles practical short-length distributed hypothesis testing (DHT) for binary sources, where theory traditionally focuses on asymptotics. It proposes three schemes built from short binary linear block codes: a truncation baseline, a binary quantizer, and a quantize-binning approach, each accompanied by exact analytical expressions for Type-I and Type-II error probabilities. Numerical results and Monte Carlo simulations show that the practical schemes, especially the quantization and quantize-binning approaches, outperform the truncation baseline and align closely with the predicted error probabilities. The work provides actionable design insights for implementing DHT in short-length regimes and outlines avenues for extending the schemes to larger lengths via interleaving and complexity reduction.

Abstract

This paper investigates practical coding schemes for Distributed Hypothesis Testing (DHT). While the literature has extensively analyzed the information-theoretic performance of DHT and established bounds on Type-II error exponents through quantize and quantize-binning achievability schemes, the practical implementation of DHT coding schemes has not yet been investigated. Therefore, this paper introduces practical implementations of quantizers and quantize-binning schemes for DHT, leveraging short-length binary linear block codes. Furthermore, it provides exact analytical expressions for Type-I and Type-II error probabilities associated with each proposed coding scheme. Numerical results show the accuracy of the proposed analytical error probability expressions, and enable to compare the performance of the proposed schemes.
Paper Structure (18 sections, 2 theorems, 23 equations, 3 figures)

This paper contains 18 sections, 2 theorems, 23 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. DHT for binary sources
  4. Error-exponent for binary DHT
  5. Short-length nature of DHT
  6. Truncation Scheme
  7. Code construction
  8. Theoretical analysis
  9. Quantization Scheme
  10. Code construction
  11. Theoretical analysis
  12. Quantize-Binning Scheme
  13. Code construction
  14. Theoretical analysis
  15. Numerical Results
  16. ...and 3 more sections

Key Result

Proposition 1

For the quantization scheme and for a threshold value $\lambda_q$, Type-I and Type-II error probabilities are given by where for $j = \gamma + \lambda - 2u$ and $0 \leq u \leq \min(\gamma,\lambda) \leq n$,

Figures (3)

  • Figure 1: Distributed hypothesis testing scheme
  • Figure 2: ROC curve for the BCH code $(31,16,7)$ user as a quantizer, compared to the truncation scheme.
  • Figure 3: ROC curve for the quantize-binning scheme built from the BCH code $(31,16,7)$ for quantization combined with the Reed-Muller code $(16,5,8)$ for binning

Theorems & Definitions (4)

  • Proposition 1
  • proof
  • Proposition 2
  • proof