Doctor of Philosophy (PhD)
Division of Electrical & Computer Engineering
In a wire tap channel, the transmitter Alice communicates with the legitimate receiver, Bob, in the presence of another receiver, Eve. The goal is to keep the wiretapper, Eve, as ignorant as possible about the information sent to Bob. For communication channels where the adversary, Eve, eavesdrops on the information sent between the legitimate users by wiretapping at the Bob's end, Wyner introduced secure encoding schemes and showed that non zero reliable transmission rate is possible in perfect secrecy. Wyner also obtained the information theoretic achievable rate equivocation region (Rb, DeltaK) for discrete memoryless wire tap channels. The rate equivocation region (Rb, DeltaK) is a trade off between the rate Rb at which information is sent by Alice to Bob, and the level of equivocation (confusion) DeltaK at the wiretapper Eve about this information.
In this dissertation, we propose an iterative algorithm to compute the rate equivocation region (Rb, DeltaK) for any finite input finite output discrete memoryless wiretap channels in Wyners model. First, we investigate the achievable region of Wyner's wire tap channel in both Wyners and Csiszar Korner form. We analyze the general form of the achievable region in both forms and show that both forms are equivalent. We also show that calculating the rate equivocation region can be reduced to the computing of a function Gamma Rb defined by Wyner.
Computing the function Gamma Rb involves convex programming and there exists no analytic closed form solution. We transform the function Gamma Rb into a minimax problem and obtain the function Gamma Rb in its parametric form. Calculating the parametric expressions in terms of the Lagrange multiplier yields a point on the Gamma Rb curve.
Next, we propose an iterative algorithm for computing the parametric expressions. The iterative procedure can be viewed as a generalization of the Arimoto Blahut method. We prove the convergence of the algorithm and derive upper and lower bounds on the optimum value as a stopping criteria of the iterative algorithm. We provide simulation results about the computation of the parametric expressions from the proposed algorithm and of the achievable rate equivocation region. We also analyze the speed of the convergence of the proposed algorithm.
We further propose an accelerated iterative algorithm to compute the parametric expressions with improved performance. The iterative procedure can be regarded as a generalization of the accelerated Arimoto Blahut algorithm. We obtain a sufficient condition of the weighted parameter and the algorithm is proved to be convergent. We compare the simulation results of the two proposed algorithms and show that the accelerated algorithm outperforms in terms of number of iterations and elapsed time for each run.
Gangula, Meena, "On the Computation of the Rate-Equivocation Region for Wyner's Wire-tap Channels" (2018). LSU Doctoral Dissertations. 4558.
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