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In this paper, we consider a scenario where a source node wishes to broadcasttwo confidential messages to two receivers, while a wire-tapper also receivesthe transmitted signal. This model is motivated by wireless communications,where individual secure messages are broadcast over open media and can bereceived by any illegitimate receiver. The secrecy level is measured by theequivocation rate at the eavesdropper. We first study the general(non-degraded) broadcast channel with an eavesdropper. We present an innerbound on the secrecy capacity region for this model. This inner bound is basedon a combination of random binning, and the Gelfand-Pinsker binning. We furtherstudy the situation in which the channels are degraded. For the degradedbroadcast channel with an eavesdropper, we present the secrecy capacity region.Our achievable coding scheme is based on Covers superposition scheme and randombinning. We refer to this scheme as the Secret Superposition Scheme. Ourconverse proof is based on a combination of the converse proof of theconventional degraded broadcast channel and Csiszar Lemma. We then assume thatthe channels are Additive White Gaussian Noise (AWGN) and show that the SecretSuperposition Scheme with Gaussian codebook is optimal. The converse proof isbased on Costas entropy power inequality. Finally, we use a broadcast strategyfor the slowly fading wire-tap channel when only the eavesdroppers channel isfixed and known at the transmitter. We derive the optimum power allocation forthe coding layers, which maximizes the total average rate.

Secrecy Rate Region of the Broadcast Channel with an Eavesdropper