Studies increasingly show that behavioral relevance alters the population representation of sensory stimuli in the sensory cortices. However, the mechanisms underlying this behavior are incompletely understood. Here, we record neuronal responses in the auditory cortex while a highly trained, awake, normal-hearing gerbil listens passively to target tones of high versus low behavioral relevance. Using an information theoretic framework, we model the overall transmission chain from acoustic input stimulus to recorded cortical response as a communication channel. To quantify how much information core auditory cortex carries about high versus low relevance sound, we then compute the mutual information of the multi-unit neuronal responses. Results show that the output over the stimulus-to-response channel can be modeled as a Poisson mixture. We derive a closed-form fast approximation for the entropy of a mixture of univariate Poisson random variables. A purely rate-code based model reveals reduced information transfer for high relevance compared to low relevance tones, hinting that changes in temporal discharge pattern may encode behavioral relevance.