# Channel Resolvability Theorems for General Sources and Channels

## TL;DR

This paper derives general formulas for channel resolvability, characterizing the minimum rate of randomness needed to approximate output distributions for general sources and channels, extending to second-order analysis.

## Contribution

It provides new formulas for channel resolvability applicable to general sources and channels, including stationary memoryless cases and second-order analysis.

## Key findings

- Formulas recapture single-letter results for stationary memoryless sources.
- Reduces to spectral sup-entropy rates when channel is identity.
- Extends analysis to second-order channel resolvability.

## Abstract

In the problem of channel resolvability, where a given output probability distribution via a channel is approximated by transforming the uniform random numbers, characterizing the asymptotically minimum rate of the size of the random numbers, called the channel resolvability, has been open. This paper derives formulas for the channel resolvability for a given general source and channel pair. We also investigate the channel resolvability in an optimistic sense. It is demonstrated that the derived general formulas recapture a single-letter formula for the stationary memoryless source and channel. When the channel is the identity mapping, the established formulas reduce to an alternative form of the spectral sup-entropy rates, which play a key role in information spectrum methods. The analysis is also extended to the second-order channel resolvability.