Gaussian Broadcast Channels with Bidirectional Conferencing Decoders and Correlated Noises

The two-user Gaussian broadcast channel (BC) with correlated noises and with decoders connected by cooperative links of finite capacities (known as conferencing decoders) is considered. A novel outer bound on the capacity region is established. For the channel with fully correlated noises (i.e., the noise correlation is either 1 or -1), the new outer bound yields exact capacity region for two cases: 1) BCs with degraded message sets; 2) BCs with one-sided conferencing from the weaker receiver to the stronger receiver. For these two cases, it is also shown that the outer bound is within half bits to the capacity region for arbitrary noise correlation. Furthermore, for the Gaussian BC with arbitrary noise correlation λ, we show that regardless of the capacities of conferencing links, a one-sided cooperative scheme (from the stronger user to the weaker one) based on decode-and-forward is sufficient to achieve the capacity region to within $\frac{1}{2}\log \left( {\frac{2}{{1 - |\lambda |}}} \right)$ bits.