Algorithms for Three and Four Dimensional Geometrical Moment Space Bounding.
CALIFORNIA UNIV LOS ANGELES DEPT OF SYSTEM SCIENCE
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The solution to many problems in communication theory takes the form of a moment of a function of a random variable. Often this moment is difficult to evaluate numerically. When this is the case, tight bounds to the true value are sought that are relatively easy to evaluate. One method of deriving such bounds is a geometrical technique that is a result of an Isomorphism Theorem from Game Theory. Recently, very useful bounds have been derived with this technique using two and some classes of three-dimensional geometries. All of these results have been analytical in nature. This report extends this work by providing algorithmic techniques for evaluating bounds produced by all classes of thre and four-dimensional geometries. In addition, a procedure for extending these algorithms to problems of dimensionality greater than four is outlined. Implementations of the three and four-dimensional algorithms are presented in appendices. Author
- Non-Radio Communications