Exact characterization of classical channel resolvability

Characterize the exact asymptotic resolvability capacity of arbitrary classical channels, i.e., determine the minimal rate of input randomness required to approximate any target output distribution to vanishing distance for every classical channel.

Background

By analogy with the quantum formulation, the classical channel resolvability task asks for the minimal rate of (essentially uniform) input randomness that allows approximation of an arbitrary output distribution through a fixed channel. While various bounds are known, a complete characterization of the asymptotic rate remains unresolved in the classical literature.

The authors highlight this gap explicitly, noting the lack of an exact asymptotic characterization for classical channel resolvability and pointing readers to information-spectrum references where the problem is discussed as open.