Exact Exponent for Soft Covering

TL;DR

This paper determines the precise exponential rates at which the soft-covering phenomenon occurs in memoryless channels under total variation, providing tighter bounds that enhance understanding and applications in information theory.

Contribution

It establishes the exact exponents for soft-covering under total variation, improving upon previous bounds and differing significantly from relative entropy-based results.

Findings

Exact exponents for soft-covering under total variation established.

Improved bounds for resolvability and secrecy exponents derived.

Distinct proof techniques from relative entropy results.

Abstract

This work establishes the exact exponents for the soft-covering phenomenon of a memoryless channel under the total variation metric when random (i.i.d. and constant-composition) channel codes are used. The exponents, established herein, are strict improvements in both directions on bounds found in the literature. This complements the recent literature establishing the exact exponents under the relative entropy metric; however, the proof techniques have significant differences, and thus, neither result trivially implies the other. The found exponents imply new and improved bounds for various problems that use soft-covering as their achievability argument, including new lower bounds for the resolvability exponent and the secrecy exponent in the wiretap channel.