Inner and Outer Bounds on the Secrecy Capacity of Degraded Broadcast Channels with RMSI and Transmitter CSI

Abstract

This paper studies the secrecy capacity of a class of degraded broadcast channels in the presence of an external eavesdropper, where a transmitter aims to deliver two independent confidential messages to two legitimate receivers. The transmitter is assumed to have non-causal access to the channel state information (CSI), and each legitimate receiver possesses prior knowledge of the other receiver's message, referred to as receiver message side information (RMSI). We consider two distinct scenarios: complementary RMSI, where each receiver knows only the other's message, and non-complementary RMSI, where the side information does not perfectly align. For both scenarios, we derive novel inner bounds on the achievable secrecy rate region and present tight outer bounds, establishing the secrecy capacity region for the considered degraded channel settings. Unlike prior works, which primarily address general broadcast settings without secrecy constraints or omit key interactions between RMSI and CSI, our results provide a complete characterization of the secure communication limits under these conditions. Moreover, we extend our analysis to the Gaussian degraded broadcast channel, highlighting the pivotal role of CSI in enhancing secure transmission performance. Our findings demonstrate that the combination of RMSI and CSI can be strategically leveraged to expand the secrecy capacity region, thus offering new insights into secure multiuser communication system design.