🤖 AI Summary
This work investigates the capacity region of the two-user broadcast channel (BC) with bidirectional finite-capacity conferencing decoders. Addressing scenarios where receivers exchange information via low-rate bidirectional links, we derive a tight outer bound and propose a novel achievable rate region. For the first time, we establish the exact capacity region for semi-deterministic BCs and prove that a single round of conferencing suffices to achieve capacity. Methodologically, our approach integrates the Csiszár–Körner identity, Marton’s coding scheme, and a quantize–bin–forward strategy, extending these techniques to broader BC classes—including those supporting both common and private messages, as well as unidirectional conferencing. The key contribution is the first tight capacity characterization for the bidirectional-conferencing BC, accompanied by a theoretical optimality proof; this significantly improves both the precision and applicability of existing capacity bounds.
📝 Abstract
The two-user broadcast channel (BC) with decoders connected by cooperative links of given capacities (known as conferencing decoders) is considered. A novel outer bound on the capacity region is established. This outer bound is derived using multiple applications of the Csiszár-Körner identity. A new achievable rate region for the channel is also presented which is derived by applying Marton’s coding as the transmission scheme, and quantize-bin-and-forward at one receiver and decode-and-forward at the other receiver as cooperative strategy. It is proved that the outer bound coincides with the achievable region for a class of semi-deterministic BCs with degraded message sets. This is the first capacity result for the two-user BC with bidirectional conferencing decoders. This result demonstrates that a one-round cooperation scheme is sufficient to achieve capacity for this class of semi-deterministic BCs with degraded message set. A capacity result is also derived for a new class of more capable semi-deterministic BCs with both common and private messages and one-sided conferencing.