Hypothesis Testing for Adversarial Channels: Chernoff–Stein Exponents
Abstract
We study the Chernoff-Stein exponent of the following binary hypothesis testing problem: Associated with each hypothesis is a set of channels. A transmitter, without knowledge of the hypothesis, chooses the vector of inputs to the channel. Given the hypothesis, from the set associated with the hypothesis, an adversary chooses channels, one for each element of the input vector. Based on the channel outputs, a detector attempts to distinguish between the hypotheses. We study the Chernoff-Stein exponent for the cases where the transmitter (i) is deterministic, (ii) may privately randomize, and (iii) shares randomness with the detector that is unavailable to the adversary. It turns out that while a memoryless transmission strategy is optimal under shared randomness, it may be strictly suboptimal when the transmitter only has private randomness.
Fields of Study & Subjects
Wireless Communication Security Techniques
Cryptography and Data Security
Adversarial Robustness in Machine Learning
Publication details
- Journal / source
- IEEE Transactions on Information Theory
- Publisher
- Institute of Electrical and Electronics Engineers (IEEE)
- Volume
- 72
- Issue
- 7
- Pages
- 5104–5121
- Publication date
- 7 May 2026
- Language
- EN