Sum-Rate Capacity for Symmetric Gaussian Multiple Access Channels with Feedback

The feedback sum-rate capacity is established for the symmetric three-user Gaussian multiple-access channel (GMAC). The main contribution is a converse bound that combines the dependence-balance argument of Hekstra and Willems (1989) with a variant of the “doubling trick” of Geng and Nair (2014). The converse bound matches the achievable sum-rate of the Fourier-Modulated Estimate Correction strategy of Kramer (2002). The proof arguments extend to GMACs with more than three users.