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

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