On the 3-Receiver Broadcast Channel with Degraded Message Sets and Confidential Messages

Abstract: In this paper, bounds to the rate-equivocation region for the general 3-receiver broadcast channel (BC) with degraded message sets, are presented for confidential messages to be kept secret from one of the receivers. This model is more general than the 2-receiver BCs with confidential messages with an external wiretapper, and the recently studied 3-receiver degraded BCs with confidential messages, since in the model studied in this paper, the conditions on the receivers are general and the wiretapper receives the common message. Wyner's code partitioning combined with double-binning is used to show the achievable rate tuples. Error probability analysis and equivocation calculation are also provided. The secure coding scheme is sufficient to provide security for the 3-receiver BC with 2 or 3 degraded message sets, for the scenarios: (i) 3 degraded message sets, where the first confidential message is sent to receivers 1 and 2 and the second confidential message is sent to receiver 1, (ii) 2 degraded message sets, where one confidential message is sent to receiver 1, and (iii) 2 degraded message sets, where one confidential message is sent to receivers 1 and 2. The proof for the outer bound is shown for the cases where receiver 1 is more capable than the wiretap receiver 3, for the first two scenarios. Under the condition that both receivers 1 and 2 are less noisy than the wiretap receiver 3, the inner and outer bounds coincide, giving the rate-equivocation region for (iii). In addition, a new outer bound for the general 3-receiver BC with 3 degraded messages is obtained.