Wiretap Channels: Implications of the More Capable Condition and Cyclic Shift Symmetry
Omur Ozel, Şennur Ulukuş
Characterization of the rate-equivocation region of a general wiretap channel involves two auxiliary random variables:U, for rate splitting andV, for channel prefixing. In this paper, we explore specific classes of wiretap channels for which the evaluation of the rate-equivocation region is simpler. We show that if the wiretap channel is more capable,V=Xis optimal and the boundary of the rate-equivocation region is achieved by varying rate splittingUalone. Conversely, we show under a mild condition that if the wiretap channel is not more capable, thenV=Xis strictly suboptimal. Next, we focus on the class of cyclic shift symmetric wiretap channels. We show that optimal rate splittingUthat achieves the boundary of the rate-equivocation region is uniform with cardinality |X| and the prefix channel between optimalUandVis expressed as cyclic shifts of the solution of an auxiliary optimization problem over a single variable. We provide a special class of cyclic shift symmetric wiretap channels for whichU=φ is optimal. We apply our results to the binary-input cyclic shift symmetric wiretap channels and thoroughly characterize the rate-equivocation regions of the BSC-BEC and BEC-BSC wiretap channels.
arXiv:1110.4613•IEEE Transactions on Information Theory•Dec 4, 2012•13 citations