A stronger soft-covering lemma and applications

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.