The Secrecy Rate Region of the Broadcast Channel

Abstract

In this paper, we consider a scenario where a source node wishes to broadcast two confidential messages for two respective receivers, while a wire-tapper also receives the transmitted signal. This model is motivated by wireless communications, where individual secure messages are broadcast over open media and can be received by any illegitimate receiver. The secrecy level is measured by equivocation rate at the eavesdropper. We first study the general (non-degraded) broadcast channel with confidential messages. We present an inner bound on the secrecy capacity region for this model. The inner bound coding scheme is based on a combination of random binning and the Gelfand-Pinsker bining. This scheme matches the Marton's inner bound on the broadcast channel without confidentiality constraint. We further study the situation where the channels are degraded. For the degraded broadcast channel with confidential messages, we present the secrecy capacity region. Our achievable coding scheme is based on Cover's superposition scheme and random binning. We refer to this scheme as Secret Superposition Scheme. In this scheme, we show that randomization in the first layer increases the secrecy rate of the second layer. This capacity region matches the capacity region of the degraded broadcast channel without security constraint. It also matches the secrecy capacity for the conventional wire-tap channel. Our converse proof is based on a combination of the converse proof of the conventional degraded broadcast channel and Csiszar lemma. Finally, we assume that the channels are Additive White Gaussian Noise (AWGN) and show that secret superposition scheme with Gaussian codebook is optimal. The converse proof is based on the generalized entropy power inequality.

12 pages, 4 figures

References in corpus (7)

• Secure Communication over Fading Channels
• Relay Channels with Confidential Messages
• The Gaussian Wiretap Channel with a Helping Interferer
• On the Secrecy Capacity of Fading Channels
• Secure Broadcasting
• Secrecy Capacity of the Wiretap Channel with Noisy Feedback
• Success Exponent of Wiretapper: A Tradeoff between Secrecy and Reliability

Cited by in corpus (5)

• The Secrecy Capacity Region of the Gaussian MIMO Multi-receiver Wiretap Channel
• Degraded Compound Multi-receiver Wiretap Channels
• Secured Communication over Frequency-Selective Fading Channels: a practical Vandermonde precoding
• Multi-receiver Wiretap Channel with Public and Confidential Messages
• A New Secret key Agreement Scheme in a Four-Terminal Network