Degraded Broadcast Channel with Side Information, Confidential Messages and Noiseless Feedback

Details Degraded Broadcast Channel with Side Information, Confidential Messages and Noiseless Feedback Degraded Broadcast Channel with Side Information, Confidential Messages and Noiseless Feedback

2012-01-13

arxiv.org/abs/1201.2859v4

Computer Science

Information Theory

This paper has been partially submitted to ISIT2012

Scientific paper

In this paper, we investigate the model of degraded broadcast channel with side information, confidential messages and noiseless feedback. This work is from Steinberg's work on the degraded broadcast channel with causal and noncausal side information, and Csisz$\acute{a}$r and K\"{o}rner's work on broadcast channel with confidential messages. In this new model, the transmitter sends a confidential message to the non-degraded receiver, and meanwhile sends a common message to both the degraded and non-degraded receivers. Moreover, the channel for the non-degraded receiver is controlled by channel state information (side information), and it is available to the transmitter in a causal manner (termed here causal side information) or noncausal manner (termed here noncausal side information). In addition, we assume that there is a noiseless feedback from the output of the channel for the non-degraded receiver to the transmitter, and it helps the transmitter and the non-degraded receiver to share a secret key, which enlarges the degraded receiver's uncertainty about the confidential message. Measuring the uncertainty by equivocation (a conditional entropy), the capacity region composed of all achievable rates-equivocation triples is determined for this new model in both causal and noncausal manners. Furthermore, the secrecy capacity in both manners is formulated, which provides the best transmission rate with perfect secrecy.

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