On the Capacity Region of the Three-Receiver Broadcast Channel With Receiver Message Cognition

This paper investigates the three-receiver (Y
₁
, Y
₂
, Y
₃
) discrete memoryless (DM) broadcast channel (BC) for eight receive message cognition settings in which the weakest receiver Y
₃
knows the message intended for the intermediate receiver Y
₂
, Y
₂
may or may not know the message intended for Y
₃
, and the strongest receiver Y
₁
knows none, one, or both of the messages intended for receivers Y
₂
and Y
₃
. For these eight settings, but for the Gaussian BC, the capacity regions were obtained previously by Asadi et al. In this paper, we establish the capacity regions for all eight cases for the class of less noisy DM BCs, thereby lifting the previously known capacity results from the Gaussian BC to the less noisy BC. To further expand the optimality results to strictly larger classes of broadcast channels, we propose a coding scheme that includes rate-splitting and indirect decoding, techniques not needed for the less noisy or Gaussian BCs, for four of the eight message cognition cases in which receiver Y
₂
knows the message intended for Y
₃
, and show that this more general scheme achieves capacity without requiring that receiver Y
₂
be stronger than Y
₃
in any sense (and when Y
₁
knows the message intended for Y
₂
, Y
₁
is not required to be stronger than Y
₂
either whereas when Y
₁
does not know the message intended for Y
₂
it is assumed that Y
₁
is more capable than Y
₂
) whereas it is assumed that Y
₁
is less noisy than Y
₃
in all four cases. Moreover, the converse proof for the second set of capacity results require both the Nair-Wang information inequality and the Csiszar sum lemma.