Distributed Hypothesis Testing over a Noisy Channel: Error-exponents Trade-off

Abstract

A distributed hypothesis testing problem with two parties, one referred to as the observer and the other as the detector, is considered. The observer observes a discrete memoryless source and communicates its observations to the detector over a discrete memoryless noisy channel. The detector observes a side-information correlated with the observer's observations, and performs a binary hypothesis test on the joint probability distribution of its own observations with that of the observer. With the objective of characterizing the performance of the hypothesis test, we obtain two inner bounds on the trade-off between the exponents of the type I and type II error probabilities. The first inner bound is obtained using a combination of a type-based quantize-bin scheme and Borade et al.'s unequal error protection scheme, while the second inner bound is established using a type-based hybrid coding scheme. These bounds extend the achievability result of Han and Kobayashi obtained for the special case of a rate-limited noiseless channel to a noisy channel. For the special case of testing for the marginal distribution of the observer's observations with no side-information at the detector, we establish a single-letter characterization of the optimal trade-off between the type I and type II error-exponents. Our results imply that a "separation" holds in this case, in the sense that the optimal trade-off between the error-exponents is achieved by a scheme that performs independent hypothesis testing and channel coding.

On Distributed Learning with Constant Communication Bits

“…for all Q X ∈ P X and Y ∈ P Y , where Π X (•) and Π Y (•) are as defined in (11), and " k " is as defined in Definition 3.…”

Strong Converse for Testing Against Independence over a Noisy channel

“…The objective is to study the trade-off between the transmission rate, and the type I and type II error probabilities in HT. This problem has been extensively studied thereafter [2]- [14]. Also, several interesting variants of the basic problem have been considered which includes extensions to multi-terminal settings [15]- [19], HT under security or privacy constraints [20]- [23], HT with lossy compression [24], HT in interactive settings [25]- [27], HT with successive refinement [28], to name a few.…”