2021/06/23 by Mustapha Hamad, Hamad, Mustapha, Michèle Wigger +3
Computer Science · Engineering · Mathematics · #Distributed Sensor Networks and Detection Algorithms #FOS: Computer and information sciences #Information Theory (cs.IT) #Statistical Methods and Inference #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.2106.12299
openalex publication_date 2021/06/23 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
Cascaded binary hypothesis testing is studied in this paper with two decision\ncenters at the relay and the receiver. All terminals have their own\nobservations, where we assume that the observations at the transmitter, the\nrelay, and the receiver form a Markov chain in this order. The communication\noccurs over two hops, from the transmitter to the relay and from the relay to\nthe receiver. Expected rate constraints are imposed on both communication\nlinks. In this work, we characterize the optimal type-II error exponents at the\ntwo decision centers under constraints on the allowed type-I error\nprobabilities. Our recent work characterized the optimal type-II error\nexponents in the special case when the two decision centers have same type-I\nerror constraints and provided an achievability scheme for the general setup.\nTo obtain the exact characterization for the general case, in this paper we\nprovide a new converse proof as well as a new matching achievability scheme.\nOur results indicate that under unequal type-I error constraints at the relay\nand the receiver, a tradeoff arises between the maximum type-II error\nprobabilities at these two terminals. Previous results showed that such a\ntradeoff does not exist under equal type-I error constraints or under general\ntype-I error constraints when a maximum rate constraint is imposed on the\ncommunication links.\n