UNIVERSITY OF CALIFORNIA, SAN DIEGO Coding and Capacities for Multidimensional Constraints
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چکیده
OF THE DISSERTATION Coding and Capacities for Multidimensional Constraints by Zsigmond Nagy Doctor of Philosophy in Electrical Engineering (Communication Theory and Systems) University of California, San Diego, 2002 Professor Kenneth Zeger, Chair A one-dimensional binary sequence satisfies the (d; k) run length constraint if the number of consecutive 0s is at most k, and between any two 1s in the sequence are at least d 0s. An n-dimensional binary array satisfies the (d; k) run length constraint if the one-dimensional (d; k) constraint is satisfied along every direction parallel to the coordinate axes. Other classes of constraints can also be defined. For example, a twodimensional checkerboard constraint is a bounded measurable set S R2 that contains the origin. A binary labeling of Z2 satisfies the checkerboard constraint S, if for every t 2 Z2 that is labeled with 1, every other point of Z2 in S + t is labeled with 0s. Constrained codes are used in digital recording applications such as magnetic and optical data storage systems, where the constraints model certain physical properties of the recording device. Every constraint reduces the average amount of information that can be stored
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