On the Gaussian MAC with Imperfect Feedback

New achievable regions are derived for the two-user additive white Gaussian multiple-access channel (MAC) with noisy feedback. We treat the general scenario as well as the symmetric setting and the partial feedback setting. Unlike previously-known achievable regions, the new regions yield sum-rates that are strictly larger than the no-feedback sum-rate capacity, irrespective of the (positive & finite) Gaussian feedback-noise variance. In the symmetric setting, our proposed coding scheme achieves sum-rates that converge to Ozarow's noiseless-feedback sum-rate capacity as the feedback-noise variance tends to zero. In the partial-feedback setting, where one of the transmitters has a perfect feedback link and the other has no feedback at all, we show that the Cover-Leung region (which was originally proposed for perfect-feedback channels but which was later shown to be achievable also with partial feedback) is not tight. This answers in the negative the question posed by van der Meulen as to whether the Cover-Leung region is tight for the Gaussian multiple-access channel with partial feedback. We also propose a coding scheme for the case where the receiver is cognizant of the realization of the noise on the feedback-link.