Capacity Bounds for Broadcast Channels With Bidirectional Conferencing Decoders

Abstract

The two-user broadcast channel (BC) with receivers connected by bidirectional cooperation links of finite capacities, known as conferencing decoders, is considered. A novel capacity region outer bound is established based on multiple applications of the Csiszár-Körner identity. Achievable rate regions are derived by using Marton’s coding as the transmission scheme, together with different combinations of decode-and-forward and quantize-bin-and-forward strategies at the receivers. It is shown that the outer bound coincides with the achievable rate region for a new class of semi-deterministic BCs with degraded message sets; for this class of channels, one-round cooperation is sufficient to achieve the capacity. Capacity result is also derived for a class of more capable semi-deterministic BCs with both common and private messages and one-sided conferencing. For the Gaussian BC with conferencing decoders, if the noises at the decoders are perfectly correlated (i.e., the correlation is either 1 or −1), the new outer bound yields exact capacity region for two cases: 1) BC with degraded message sets; 2) BC with one-sided conferencing from the weaker receiver to the stronger receiver. When the noises have arbitrary correlation, the outer bound is shown to be within half a bit from the capacity region for these same two cases. Finally, for the general Gaussian BC, a one-sided cooperation scheme based on decode-and-forward from the stronger receiver to the weaker receiver is shown to achieve the capacity region to within $\frac {1}{2}\log \left ({{\frac {2}{1-|\lambda |}}}\right)$ bits, where $\lambda $ is the noise correlation. An interesting implication of these results is that for a Gaussian BC with perfectly negatively correlated noises and conferencing decoders with finite cooperation link capacities, it is possible to achieve a strictly positive rate using only an infinitesimal amount of transmit power.