Exact Soft-Covering Exponent

This work establishes the exact exponent for the soft-covering phenomenon of a memoryless channel under the total variation metric. The exponent, established herein, is a strict improvement (in both directions) on bounds found in the literature. This complements the recent literature establishing the exact exponent under the relative entropy metric; however, the proof techniques have significant differences, neither bound trivially implies the other, and we show that the total variation metric yields a more precise high-probability claim, in addition to the standard expected value claim. This result implies 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.