This paper investigates the three-receiver (Y1, Y2, Y3) discrete memoryless (DM) broadcast channel (BC) for eight receive message cognition settings in which the weakest receiver Y3 knows the message intended for the intermediate receiver Y2, Y2 may or may not know the message intended for Y3, and the strongest receiver Y1 knows none, one, or both of the messages intended for receivers Y2 and Y3. 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 Y2 knows the message intended for Y3, and show that this more general scheme achieves capacity without requiring that receiver Y2 be stronger than Y3 in any sense (and when Y1 knows the message intended for Y2 , Y1 is not required to be stronger than Y2 either whereas when Y1 does not know the message intended for Y2 it is assumed that Y1 is more capable than Y2) whereas it is assumed that Y1 is less noisy than Y3 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.
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