Coding for classical-quantum channels with rate limited side information at the encoder: An information-spectrum approach

TL;DR

This paper determines the capacity region of a classical-quantum channel with rate-limited side information at the encoder, using an information-spectrum approach to generalize the Gel'fand-Pinsker problem.

Contribution

It introduces a novel information-spectrum framework to characterize the capacity of classical-quantum channels with limited side information at the encoder.

Findings

Capacity region expressed via spectral-sup classical mutual information rate.

Capacity region expressed via spectral-inf quantum mutual information rate.

First capacity characterization for this hybrid classical-quantum setting.

Abstract

We study the hybrid classical-quantum version of the channel coding problem for the famous Gel'fand-Pinsker channel. In the classical setting for this channel the conditional distribution of the channel output given the channel input is a function of a random parameter called the channel state. We study this problem when a rate limited version of the channel state is available at the encoder for the classical-quantum Gel'fand-Pinsker channel. We establish the capacity region for this problem in the information-spectrum setting. The capacity region is quantified in terms of spectral-sup classical mutual information rate and spectral-inf quantum mutual information rate.