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Abstract: In this paper, bounds to the rate-equivocation region for the general3-receiver broadcast channel BC with degraded message sets, are presented forconfidential messages to be kept secret from one of the receivers. This modelis more general than the 2-receiver BCs with confidential messages with anexternal wiretapper, and the recently studied 3-receiver degraded BCs withconfidential messages, since in the model studied in this paper, the conditionson the receivers are general and the wiretapper receives the common message.Wyner-s code partitioning combined with double-binning is used to show theachievable rate tuples. Error probability analysis and equivocation calculationare also provided. The secure coding scheme is sufficient to provide securityfor the 3-receiver BC with 2 or 3 degraded message sets, for the scenarios: i3 degraded message sets, where the first confidential message is sent toreceivers 1 and 2 and the second confidential message is sent to receiver 1,ii 2 degraded message sets, where one confidential message is sent toreceiver 1, and iii 2 degraded message sets, where one confidential messageis sent to receivers 1 and 2. The proof for the outer bound is shown for thecases where receiver 1 is more capable than the wiretap receiver 3, for thefirst two scenarios. Under the condition that both receivers 1 and 2 are lessnoisy than the wiretap receiver 3, the inner and outer bounds coincide, givingthe rate-equivocation region for iii. In addition, a new outer bound for thegeneral 3-receiver BC with 3 degraded messages is obtained.



Author: Li-Chia Choo, Kai-Kit Wong

Source: https://arxiv.org/







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