Abstract
By proving a strong converse theorem, we strengthen the weak converse result by Salehkalaibar, Wigger and Wang (2017) concerning hypothesis testing against independence over a two-hop network with communication constraints. Our proof follows by combining two recently-proposed techniques for proving strong converse theorems, namely the strong converse technique via reverse hypercontractivity by Liu, van Handel, and Verdú (2017) and the strong converse technique by Tyagi and Watanabe (2018), in which the authors used a change-of-measure technique and replaced hard Markov constraints with soft information costs. The techniques used in our paper can also be applied to prove strong converse theorems for other multiterminal hypothesis testing against independence problems.
Highlights
Motivated by situations where the source sequence is not available directly and can only be obtained through limited communication with the data collector, Ahlswede and Csiszár [1] proposed the problem of hypothesis testing with a communication constraint
Before presenting the proof of Theorem 2, in this subsection, we briefly review the two strong converse techniques that we judiciously combine in this work, namely the change-of-measure technique by Tyagi and Watanabe [13] and the hypercontractivity technique by Liu et al [12]
In the rest of this section, we present the proof of strong converse theorem for the hypothesis testing over the two-hop network
Summary
Motivated by situations where the source sequence is not available directly and can only be obtained through limited communication with the data collector, Ahlswede and Csiszár [1] proposed the problem of hypothesis testing with a communication constraint. The encoder has access to one source sequence X n and transmits a compressed version of it to the decoder at a limited rate. Is generated i.i.d. from one of the two distributions and needs to determine which distribution the pair of sequences is generated from The goal in this problem is to study the tradeoff between the compression rate and the exponent of the type-II error probability under the constraint that the type-I error probability is either vanishing or non-vanishing. For the special case of testing against independence, Ahlswede and Csiszár provided an exact characterization of the rate-exponent tradeoff. They derived the so-called strong converse theorem for the problem. The characterization the rate-exponent tradeoff for the general case (even in the absence of a strong converse) remains open till date
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