TL;DR
This paper strengthens Wyner's soft-covering lemma by proving that a random codebook achieves soft-covering with high probability and an extremely small failure probability, enhancing its applicability in information theory.
Contribution
It provides a high-probability version of the soft-covering lemma, moving beyond expected value analysis to enable more robust information-theoretic applications.
Findings
Failure probability is doubly-exponentially small in block-length
High-probability guarantees improve union bound applications
Strengthens the theoretical foundation for security and coding proofs
Abstract
Wyner's soft-covering lemma is a valuable tool for achievability proofs of information theoretic security, resolvability, channel synthesis, and source coding. The result herein sharpens the claim of soft-covering by moving away from an expected value analysis. Instead, a random codebook is shown to achieve the soft-covering phenomenon with high probability. The probability of failure is doubly-exponentially small in the block-length, enabling more powerful applications through the union bound.
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