  The two-user broadcast channel (BC) with receivers 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 Csisz\'{a}r-K\"{o}rner identity. New
achievable rate regions are also presented. A first achievable rate region is
derived by applying Marton's coding as the transmission scheme, and
quantize-bin-and-forward at one receiver first and then a combination of
decode-and-forward and quantize-bin-and-forward at the other receiver as
cooperative strategy. A second achievable rate region is given by applying a
combination of decode-and-forward and quantize-bin-and-forward at one receiver
first and then quantize-bin-and-forward at the other receiver. It is proved
that the outer bound coincides with the first achievable rate 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. 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. For the Gaussian BC with conferencing decoders, if the noises at
the decoders are fully correlated (i.e., the 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. An interesting consequence of these results
is that for a Gaussian BC with fully negatively correlated noises and
conferencing decoders of fixed cooperation link capacities, it is possible to
achieve a positive rate bounded away from zero using only infinitesimal amount
of transmit power.
