Sum-Capacity for Symmetric Finite-State Gaussian Multiple Access Channel with Delayed Feedback

In this paper, the sum-capacity of the symmetric finite-state Gaussian multiple access channel (FS-GMAC) with delayed feedback is determined, where the channel state is perfectly obtained by the receiver, and the receiver sends the state and channel output back to the two transmitters through two noiseless feedback channel after same time delay. We first propose a linear-feedback coding scheme for this model, which is based on multiplexing coding and a variant of Schalkwijk- Kailath scheme, and derive the corresponding achievable sum-rate. Then, by establishing an upper bound on the sum-capacity of the same model, we further show that the proposed scheme is capacity-achieving.