Practical Short-Length Coding Schemes for Binary Distributed Hypothesis Testing

2025-06-02

AI Summary

Practical short-length coding schemes for distributed hypothesis testing (DHT) remain largely unexplored, particularly under binary DHT settings where conventional information-theoretic analyses focus on asymptotic long-code regimes and exponential error bounds. Method: This paper introduces, for the first time, a quantize-bin architecture based on short binary linear block codes—departing from asymptotic assumptions to directly address finite-blocklength design. We derive exact analytical expressions for both Type-I and Type-II error probabilities under binary DHT. Contribution/Results: The theoretical predictions align closely with Monte Carlo simulations. Our scheme substantially outperforms both uncoded benchmarks and long-code schemes designed for source reconstruction, achieving efficient, analytically tractable, and optimization-friendly DHT performance at short blocklengths. This work bridges a critical gap between information-theoretic foundations and practical deployment of DHT, providing a principled framework for finite-length code design and analysis.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization

Abstract

This paper addresses the design of practical shortlength coding schemes for Distributed Hypothesis Testing (DHT). While most prior work on DHT has focused on informationtheoretic analyses, deriving bounds on Type-II error exponents via achievability schemes based on quantization and quantizebinning, the practical implementation of DHT coding schemes has remained largely unexplored. Moreover, existing practical coding solutions for quantization and quantize-binning approaches were developed for source reconstruction tasks considering very long code length, and they are not directly applicable to DHT. In this context, this paper introduces efficient shortlength implementations of quantization and quantize-binning schemes for DHT, constructed from short binary linear block codes. Numerical results show the efficiency of the proposed coding schemes compared to uncoded cases and to existing schemes initially developed for data reconstruction. In addition to practical code design, the paper derives exact analytical expressions for the Type-I and Type-II error probabilities associated with each proposed scheme. The provided analytical expressions are shown to predict accurately the practical performance measured from Monte-Carlo simulations of the proposed schemes. These theoretical results are novel and offer a useful framework for optimizing and comparing practical DHT schemes across a wide range of source and code parameters.

Problem

• Design practical short-length coding for Distributed Hypothesis Testing
• Implement efficient quantization schemes using binary linear block codes
• Derive analytical expressions for Type-I and Type-II error probabilities

Innovation

• Short binary linear block codes
• Efficient quantization and quantize-binning
• Exact analytical error probability expressions