Wiretap Channels: Implications of the More Capable Condition and Cyclic Shift Symmetry

Details Wiretap Channels: Implications of the More Capable Condition and Cyclic Shift Symmetry Wiretap Channels: Implications of the More Capable Condition and Cyclic Shift Symmetry

2011-10-20

arxiv.org/abs/1110.4613v1

Computer Science

Information Theory

Submitted to IEEE Transactions on Information Theory, October 2011

Scientific paper

Characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables: U, for rate splitting and V, for channel prefixing. Evaluation of regions involving auxiliary random variables is generally difficult. In this paper, we explore specific classes of wiretap channels for which the expression and evaluation of the rate-equivocation region are simpler. In particular, we show that when the main channel is more capable than the eavesdropping channel, V=X is optimal and the boundary of the rate-equivocation region can be achieved by varying U alone. Conversely, we show under a mild condition that if the main receiver is not more capable, then V=X is strictly suboptimal. Next, we focus on the class of cyclic shift symmetric wiretap channels. We explicitly determine the optimal selections of rate splitting U and channel prefixing V that achieve the boundary of the rate-equivocation region. We show that optimal U and V are determined via cyclic shifts of the solution of an auxiliary optimization problem that involves only one auxiliary random variable. In addition, we provide a sufficient condition for cyclic shift symmetric wiretap channels to have U=\phi as an optimal selection. Finally, we apply our results to the binary-input cyclic shift symmetric wiretap channels. We solve the corresponding constrained optimization problem by inspecting each point of the I(X;Y)-I(X;Z) function. We thoroughly characterize the rate-equivocation regions of the BSC-BEC and BEC-BSC wiretap channels. In particular, we find that U=\phi is optimal and the boundary of the rate-equivocation region is achieved by varying V alone for the BSC-BEC wiretap channel.

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