The Three-Receiver Broadcast Channel with Degraded Message Sets and Confidential Messages

In this paper, bounds to the secrecy capacity region for the general 3-receiver broadcast channel with 3 degraded message sets, are presented for confidential messages sent to be kept secret from one of the receivers. This model is a more general model than 2-receiver broadcast channels with confidential messages with an external wiretapper, and recently studied 3-receiver degraded broadcast channels with confidential messages, since the conditions on the receivers are general and wiretapper receives the common message. Wyner’s code partitioning combined with double-binning is used to show achievable rate tuples. Error probability analysis and equivocation calculation are also provided. The proof for the outer bound is shown for three cases: the general case; under the condition that receiver 1 is less noisy than receiver 3, the wiretapper; and under the condition that both receivers 1 and 2 are less noisy than the wiretapper, where the inner and outer bounds coincide, giving the secrecy capacity of the special case of a 3-receiver BC with 2 degraded message sets.