Linear-feedback MAC-BC duality for correlated BC-noises, and iterative coding

In this paper, we show that for the two-user Gaussian broadcast channel with correlated noises and perfect feedback the largest region that can be achieved by linear-feedback schemes equals the largest region that can be achieved over a dual multi-access channel when in this latter the channel inputs are subject to a non-standard sum-power constraint that depends on the BC-noise correlation. Combining this new duality result with Ozarow's MAC-scheme gives us an elegant achievable region for the Gaussian BC with correlated noises. We then present a constructive iterative coding scheme for the non-symmetric Gaussian BC with uncorrelated noises that is sum-rate optimal among all linear-feedback schemes. This coding scheme shows that the connection between the MAC and the BC optimal schemes is tighter than what is suggested by our duality result on achievable rates. In fact, it is linear-feedback sum-rate optimal to use Ozarow MAC-encoders and MAC-decoders- rearranged-to code over the BC.