AEP of Output when Rate is above capacity: The Gaussian case

The output distribution of a Gaussian channel, when the rate is above capacity, is investigated. It is shown that there is an asymptotic equipartition property (AEP) of the typical output sequences, independently of the specific codebook used, as long as the codebook is typical according to the standard random codebook generation. This equipartition of the typical output sequences is caused by the mixup of input sequences when there are too many of them, namely, when the rate is above capacity. This discovery may shed some light on the optimal design of the compress-and-forward relay schemes.