Distributed Sequential Hypothesis Testing With Zero-Rate Compression

TL;DR

This paper studies sequential hypothesis testing in a single-sensor setup with zero-rate communication, characterizing the optimal error exponents and showing they match fixed-length testing under similar constraints.

Contribution

It provides the first characterization of the optimal error exponent for sequential testing with zero-rate feedback, aligning it with fixed-length testing results.

Findings

Optimal error exponent derived for sequential testing with zero-rate feedback.

The exponent matches that of fixed-length hypothesis testing under the same communication constraints.

Analysis includes the case where the expected number of requests is unbounded as n grows.

Abstract

In this paper, we consider sequential testing over a single-sensor, a single-decision center setup. At each time instant $t$, the sensor gets $k$ samples $(k>0)$ and describes the observed sequence until time $t$ to the decision center over a zero-rate noiseless link. The decision center sends a single bit of feedback to the sensor to request for more samples for compression/testing or to stop the transmission. We have characterized the optimal exponent of type-II error probability under the constraint that type-I error probability does not exceed a given threshold $\epsilon\in (0,1)$ and also when the expectation of the number of requests from decision center is smaller than $n$ which tends to infinity. Interestingly, the optimal exponent coincides with that for fixed-length hypothesis testing with zero-rate communication constraints.