Practical Short-Length Coding Schemes for Binary Distributed Hypothesis Testing

Abstract

This paper addresses the design of practical short-length coding schemes for Distributed Hypothesis Testing (DHT). While most prior work on DHT has focused on information-theoretic analyses—deriving bounds on Type-II error exponents via achievability schemes based on quantization and quantize-binning—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 lengths, and they are not directly applicable to DHT. In this context, this paper introduces efficient short-length 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.