Capacity Theorems for the Cognitive Radio Channel with Confidential Messages

Abstract: As a brain inspired wireless communication scheme, cognitive radio is a novel approach to promote the efficient use of the scarce radio spectrum by allowing some users called cognitive users to access the under-utilized spectrum licensed out to the primary users. Besides highly reliable communication and efficient utilization of the radio spectrum, the security of information transmission against eavesdropping is critical in the cognitive radios for many potential applications. In this paper, this problem is investigated from an information theoretic viewpoint. Capacity limits are explored for the Cognitive Radio Channel (CRC) with confidential messages. As an idealized information theoretic model for the cognitive radio, this channel includes two transmitters which send independent messages to their corresponding receivers such that one transmitter, i.e., the cognitive transmitter, has access non-causally to the message of the other transmitter, i.e., the primary transmitter. The message designated to each receiver is required to be kept confidential with respect to the other receiver. The secrecy level for each message is evaluated using the equivocation rate. Novel inner and outer bounds for the capacity-equivocation region are established. It is shown that these bounds coincide for some special cases. Specifically, the capacity-equivocation region is derived for a class of less-noisy CRCs and also a class of semi-deterministic CRCs. For the case where only the message of the cognitive transmitter is required to be kept confidential, the capacity-equivocation region is also established for the Gaussian CRC with weak interference.