An Information-Spectrum Approach to Distributed Hypothesis Testing for General Sources

TL;DR

This paper develops a general information-spectrum framework for distributed hypothesis testing with complex, non-i.i.d. sources, providing formulas for error exponents and demonstrating the approach with specific source models.

Contribution

It introduces an information-spectrum approach to DHT that handles non-i.i.d., non-stationary, and non-ergodic sources, extending existing i.i.d. results.

Findings

Derived general formulas for Type-II error exponents.

Showed quantize-and-binning achieves the error trade-off.

Provided explicit error exponents for Gaussian and stationary sources.

Abstract

This paper investigates Distributed Hypothesis testing (DHT), in which a source $\mathbf{X}$ is encoded given that side information $\mathbf{Y}$ is available at the decoder only. Based on the received coded data, the receiver aims to decide on the two hypotheses $H_0$ or $H_1$ related to the joint distribution of $\mathbf{X}$ and $\mathbf{Y}$. While most existing contributions in the literature on DHT consider i.i.d. assumptions, this paper assumes more generic, non-i.i.d., non-stationary, and non-ergodic sources models. It relies on information-spectrum tools to provide general formulas on the achievable Type-II error exponent under a constraint on the Type-I error. The achievability proof is based on a quantize-and-binning scheme. It is shown that with the quantize-and-binning approach, the error exponent boils down to a trade-off between a binning error and a decision error, as already observed for the i.i.d. sources. The last part of the paper provides error exponents for particular source models, \emph{e.g.}, Gaussian, stationary, and ergodic models.