We study the sum-rate capacity of the two-user white Gaussian multiple-access channel when the encoders have access to noisy feedback from the channel output. The feedback links are assumed to be corrupted by independent white Gaussian noise sequences.
We propose an encoding scheme for the symmetric setting where both channel input sequences are subject to the same average power constraint and where the noise variances on the feedback links are equal. The encoding scheme achieves a sum-rate which for any (finite) feedback noise variance is strictly greater than the sum-rate capacity of the Gaussian MAC without feedback. This result extends to the case of unequal power constraints, to multiple users or to the case when the noise sequences on the two feedback links are correlated.
In the limit when the feedback noise variance tends to zero the achievable sun-rate of the proposed scheme converges to the perfect-feedback sum-rate capacity.