MAC-BC duality with linear-feedback schemes

We show that for the multi-antenna Gaussian MAC and BC with perfect feedback, the largest achievable regions with linear-feedback schemes (called linear-feedback capacity regions) coincide when the same total input-power constraint is imposed on both channels and when the MAC channel matrices are the transposes of the BC channel matrices. In the two-user case, when either transmitters or receiver are single-antenna, the capacity region for the Gaussian MAC is known and the capacity-achieving scheme is a linear-feedback scheme. With our results we can thus determine the linear-feedback capacity region of the two-user Gaussian BC when either transmitter or receivers are single-antenna. For these cases we can also identify the linear-feedback schemes that achieve the linear-feedback capacity. Our results also extend to a partial-feedback setup where only a subset of the feedback links are present.