We study distributed hypothesis testing under a covertness constraint in the non-alert situation, which requires that under the null-hypothesis an external warden be unable to detect whether communication between the sensor and the decision center is taking place. We characterize the achievable Stein exponent of this setup when the channel from the sensor to the decision center is a partially-connected discrete memoryless channel (DMC), i.e., when certain output symbols can only be induced by some of the inputs. The Stein-exponent in this case, does not depend on the specific transition law of the DMC and equals Shalaby and Papamarcou's exponent without a warden but where the sensor can send $k$ noise-free bits to the decision center, for $k$ a function that is sublinear in the observation length $n$. For fully-connected DMCs, we propose an achievable Stein-exponent and show that it can improve over the local exponent at the decision center. All our coding schemes do not require that the sensor and decision center share a common secret key, as commonly assumed in covert communication. Moreover, in our schemes the divergence covertness constraint vanishes (almost) exponentially fast in the obervation length $n$, again, an atypical behaviour for covert communication.

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.

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.