MMSE interference in Gaussian channels

We consider the scalar Gaussian channel, and address the problem of maximizing the average mutual information of a power constraint n component (n → ∞) input random vector at a given signal-to-noise ratio (snr), satisfying a minimum mean square error (MMSE) constraint at another lower snr value. We use the MMSE as an effective interference (disturbance) measure, motivated by interference networks, where codes are expected not only to optimize performance for the intended user but inflict minimum interference on other users. We show via the information-estimation relation, that superposition coding is optimal in this respect, providing further intuition to the effectiveness of the Han-Kobayashi coding strategy on the interference channel, and performance of ´bad´ codes. Moreover, the MMSE function of those codes, attaining the best rate at some snr, subjected to a prescribed MMSE demand at some other snr, is completely defined for all snr, and is the one obtained by the corresponding superposition codebooks. Extensions to two MMSE constraints, are discussed, and compared to the results for a mutual information disturbance measure. Some challenges for this class of interference problems will also be discussed.