Another Proof for the Secrecy Capacity of the K-Receiver Broadcast Channel With Confidential Messages

The secrecy capacity region for the K-receiver degraded broadcast channel (BC) is given for confidential messages sent to the receivers and to be kept secret from an external wiretapper. Superposition coding and Wyner´s random code partitioning are used to show the achievable rate tuples. Error probability analysis and equivocation calculation are also provided. In the converse proof, a new definition for the auxiliary random variables is used, which is different from either the case of the two-receiver BC without common message or the K-receiver BC with common message, both with an external wiretapper, or the K -receiver BC without a wiretapper.