Capacity Bounds for Broadcast Channels with Bidirectional Conferencing Decoders

TL;DR

This paper derives new capacity bounds and achievable rate regions for broadcast channels with bidirectional conferencing decoders, including Gaussian cases with correlated noises, showing when capacity can be exactly achieved or approximated.

Contribution

It introduces a novel outer bound for the capacity region using Csiszár-Körner identities and characterizes capacity for certain semi-deterministic and Gaussian broadcast channels with conferencing.

Findings

Outer bound matches achievable rates for semi-deterministic BCs with degraded message sets.

Capacity is exactly achieved for some semi-deterministic BCs with one-round cooperation.

For Gaussian BCs with correlated noises, the bounds are tight or within half a bit of capacity.

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 Csisz\'{a}r-K\"{o}rner 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., correlation is either 1 or -1), the new outer bound yields exact capacity region for two cases: i) BC with degraded message sets; ii) 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 $\frac{1}{2}\log (\frac{2}{1-|\lambda|})$ 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.