The individual secrecy capacity of degraded multi-receiver wiretap broadcast channels

We study secure communication over a degraded wiretap broadcast channel with multiple receivers and an eavesdropper. We consider two different secrecy measures: the traditional joint secrecy where the mutual information leakage of all messages must be small; and individual secrecy where the sum of the information leakage of each individual message must be small. At first, we investigate the joint secrecy criterion, where we present the capacity region established before and provide a simpler converse proof. We then consider the individual secrecy criterion and establish its capacity region, by combining the techniques of wiretap random coding and Shannon's one time pad principle. Our results indicate that the individual secrecy capacity region is bigger than the joint one. Further, we show that the established capacity regions are valid for any degraded wiretap broadcast channel, regardless of the degradedness order of the eavesdropper. Finally, we extend our results to Gaussian channels.