Sreekumar S, Gündüz D. Distributed Hypothesis Testing over a Noisy Channel: Error-Exponents Trade-Off.
ENTROPY (BASEL, SWITZERLAND) 2023;
25:304. [PMID:
36832670 PMCID:
PMC9954905 DOI:
10.3390/e25020304]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 12/28/2022] [Revised: 01/25/2023] [Accepted: 01/31/2023] [Indexed: 06/18/2023]
Abstract
A two-terminal distributed binary hypothesis testing problem over a noisy channel is studied. The two terminals, called the observer and the decision maker, each has access to n independent and identically distributed samples, denoted by U and V, respectively. The observer communicates to the decision maker over a discrete memoryless channel, and the decision maker performs a binary hypothesis test on the joint probability distribution of (U,V) based on V and the noisy information received from the observer. The trade-off between the exponents of the type I and type II error probabilities is investigated. Two inner bounds are obtained, one using a separation-based scheme that involves type-based compression and unequal error-protection channel coding, and the other using a joint scheme that incorporates type-based hybrid coding. The separation-based scheme is shown to recover the inner bound obtained by Han and Kobayashi for the special case of a rate-limited noiseless channel, and also the one obtained by the authors previously for a corner point of the trade-off. Finally, we show via an example that the joint scheme achieves a strictly tighter bound than the separation-based scheme for some points of the error-exponents trade-off.
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