75,579 research outputs found
Efficient Numerical Methods for Secrecy Capacity of Gaussian MIMO Wiretap Channel
This paper presents two different low-complexity methods for obtaining the
secrecy capacity of multiple-input multiple-output (MIMO) wiretap channel
subject to a sum power constraint (SPC). The challenges in deriving
computationally efficient solutions to the secrecy capacity problem are due to
the fact that the secrecy rate is a difference of convex functions (DC) of the
transmit covariance matrix, for which its convexity is only known for \emph{the
degraded case}. In the first method, we capitalize on the accelerated DC
algorithm, which requires solving a sequence of convex subproblems. In
particular, we show that each subproblem indeed admits a water-filling
solution. In the second method, based on the equivalent convex-concave
reformulation of the secrecy capacity problem, we develop a so-called partial
best response algorithm (PBRA). Each iteration of the PBRA is also done in
closed form. Simulation results are provided to demonstrate the superior
performance of the proposed methods.Comment: arXiv admin note: substantial text overlap with arXiv:2012.0566
Multigrid elliptic equation solver with adaptive mesh refinement
In this paper we describe in detail the computational algorithm used by our
parallel multigrid elliptic equation solver with adaptive mesh refinement. Our
code uses truncation error estimates to adaptively refine the grid as part of
the solution process. The presentation includes a discussion of the orders of
accuracy that we use for prolongation and restriction operators to ensure
second order accurate results and to minimize computational work. Code tests
are presented that confirm the overall second order accuracy and demonstrate
the savings in computational resources provided by adaptive mesh refinement.Comment: 12 pages, 9 figures, Modified in response to reviewer suggestions,
added figure, added references. Accepted for publication in J. Comp. Phy
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