The major anatomical characteristics of the main axis of the basal ganglia are: (1) Numerical reduction in the number of neurons across layers of the feed-forward network, (2) lateral inhibitory connections within the layers, and (3) neuro-modulatory effects of dopamine and acetylcholine, both on the basal ganglia neurons and on the efficacy of information transmission along the basal ganglia axis. We recorded the simultaneous activity of neurons in the output stages of the basal ganglia as well as the activity of dopaminergic and cholinergic neurons during the performance of a probability decision-making task. We found that the functional messages of the cholinergic and dopaminergic neurons differ, and that the cholinergic message is less specific than that of the dopaminergic neurons. The output stage of the basal ganglia showed uncorrelated neuronal activity. We conclude that despite the huge numerical reduction from the cortex to the output nuclei of the basal ganglia, the activity of these nuclei represents an optimally compressed (uncorrelated) version of distinctive features of cortical information.