Broadcast Channels with Privacy Leakage Constraints

The broadcast channel (BC) with one common and two private messages with leakage constraints is studied, where leakage rate refers to the normalized mutual information between a message and a channel symbol string. Each private message is destined for a different user and the leakage rate to the other receiver must satisfy a constraint. This model captures several scenarios concerning secrecy, i.e., when both, either or neither of the private messages are secret. Inner and outer bounds on the leakage-capacity region are derived when the eavesdropper knows the codebook. The inner bound relies on a Marton-like code construction and the likelihood encoder. A Uniform Approximation Lemma is established that states that the marginal distribution induced by the encoder on each of the bins in the Marton codebook is approximately uniform. Without leakage constraints the inner bound recovers Marton's region and the outer bound reduces to the UVW-outer bound. The bounds match for semi-deterministic (SD) and physically degraded (PD) BCs, as well as for BCs with a degraded message set. The leakage-capacity regions of the SD-BC and the BC with a degraded message set recover past results for different secrecy scenarios. A Blackwell BC example illustrates the results and shows how its leakage-capacity region changes from the capacity region without secrecy to the secrecy-capacity regions for different secrecy scenarios

Individual Secrecy for the Broadcast Channel

This paper studies the problem of secure communication over broadcast channels under the individual secrecy constraints. That is, the transmitter wants to send two independent messages to two legitimate receivers in the presence of an eavesdropper, while keeping the eavesdropper ignorant of each message (i.e., the information leakage from each message to the eavesdropper is made vanishing). Building upon Carleial-Hellman's secrecy coding, Wyner's secrecy coding, the frameworks of superposition coding and Marton's coding together with techniques such as rate splitting and indirect decoding, achievable rate regions are developed. The proposed regions are compared with those satisfying joint secrecy and without secrecy constraints, and the individual secrecy capacity regions for special cases are characterized. In particular, capacity region for the deterministic case is established, and for the Gaussian model, a constant gap (i.e., 0.5 bits within the individual secrecy capacity region) result is obtained. Overall, when compared with the joint secrecy constraint, the results allow for trading-off secrecy level and throughput in the system.Comment: 49 pages, 13 figures, this paper was presented in part at IEEE International Symposium on Information Theory, Hong Kong, Jun. 201