Output statistics, equivocation, and state masking

Ligong Wang; Ligong Wang

doi:10.3934/math.2025590

AIMS Mathematics

2025, Volume 10, Issue 6: 13151-13165. doi: 10.3934/math.2025590

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Research article Special Issues

Output statistics, equivocation, and state masking

Ligong Wang ^,

Department of Information Technology and Electrical Engineering, ETH Zurich, 8092 Zurich, Switzerland

Received: 19 March 2025 Revised: 26 May 2025 Accepted: 04 June 2025 Published: 09 June 2025
MSC : 94A15, 94A17, 94A24, 94A40

Given a discrete memoryless channel and a target distribution on its output alphabet, one wishes to construct a length-$ n $ rate-$ R $ codebook such that the output distribution—computed over a codeword that is chosen uniformly at random—should be close to the $ n $-fold tensor product of the target distribution. Here "close" means that the relative entropy between the output distribution and said $ n $-fold product should be small. We characterize the smallest achievable relative entropy divided by $ n $ as $ n $ tends to infinity. We then demonstrate two applications of this result. The first application is an alternative proof of the achievability of the rate-equivocation region of the wiretap channel. The second application is a new capacity result for communication subject to state masking in the scenario where the decoder has access to channel-state information.
- relative entropy,
- soft covering,
- approximation of output statistics,
- equivocation,
- wiretap channel,
- state masking
Citation: Ligong Wang. Output statistics, equivocation, and state masking[J]. AIMS Mathematics, 2025, 10(6): 13151-13165. doi: 10.3934/math.2025590

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Abstract

Given a discrete memoryless channel and a target distribution on its output alphabet, one wishes to construct a length-$ n $ rate-$ R $ codebook such that the output distribution—computed over a codeword that is chosen uniformly at random—should be close to the $ n $-fold tensor product of the target distribution. Here "close" means that the relative entropy between the output distribution and said $ n $-fold product should be small. We characterize the smallest achievable relative entropy divided by $ n $ as $ n $ tends to infinity. We then demonstrate two applications of this result. The first application is an alternative proof of the achievability of the rate-equivocation region of the wiretap channel. The second application is a new capacity result for communication subject to state masking in the scenario where the decoder has access to channel-state information.

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