TY - GEN

T1 - Binary Hypothesis Testing with Deterministic Finite-Memory Decision Rules

AU - Berg, Tomer

AU - Ordentlich, Or

AU - Shayevitz, Ofer

N1 - Publisher Copyright:
© 2020 IEEE.

PY - 2020/6

Y1 - 2020/6

N2 - In this paper we consider the problem of binary hypothesis testing with finite memory systems. Let X 1 , X 2 ,. be a sequence of independent identically distributed Bernoulli random variables, with expectation p under {{\mathcal{H}}-0} and q under {{\mathcal{H}}-1}. Consider a finite-memory deterministic machine with S states that updates its state M n {1,2,., S} at each time according to the rule M n = f(M n-1 , X n ), where f is a deterministic time-invariant function. Assume that we let the process run for a very long time (n→∞), and then make our decision according to some mapping from the state space to the hypothesis space. The main contribution of this paper is a lower bound on the Bayes error probability P e of any such machine. In particular, our findings show that the ratio between the maximal exponential decay rate of P e with S for a deterministic machine and for a randomized one, can become unbounded, complementing a result by Hellman.

AB - In this paper we consider the problem of binary hypothesis testing with finite memory systems. Let X 1 , X 2 ,. be a sequence of independent identically distributed Bernoulli random variables, with expectation p under {{\mathcal{H}}-0} and q under {{\mathcal{H}}-1}. Consider a finite-memory deterministic machine with S states that updates its state M n {1,2,., S} at each time according to the rule M n = f(M n-1 , X n ), where f is a deterministic time-invariant function. Assume that we let the process run for a very long time (n→∞), and then make our decision according to some mapping from the state space to the hypothesis space. The main contribution of this paper is a lower bound on the Bayes error probability P e of any such machine. In particular, our findings show that the ratio between the maximal exponential decay rate of P e with S for a deterministic machine and for a randomized one, can become unbounded, complementing a result by Hellman.

UR - http://www.scopus.com/inward/record.url?scp=85090409053&partnerID=8YFLogxK

U2 - 10.1109/ISIT44484.2020.9174505

DO - 10.1109/ISIT44484.2020.9174505

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AN - SCOPUS:85090409053

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 1259

EP - 1264

BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 21 July 2020 through 26 July 2020

ER -