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Abstract
This report deals with constrained coding in two dimensions. We describe the theory of constrained fields as a framework for addressing some of the challenges of code construction for advanced data storage devices that treat the recording media as a surface, rather than a series of tracks. The important concept of entropy is introduced. In general, the entropy of a constrained field is not readily computable, but we give a series of upper and lower bounds based on one dimensional techniques. We discuss the use of a Pickard probability model for constrained fields. The novelty lies in using a first order model to model higher order constraints by the use of an alphabet extension. We present an iterative method that based on a set of conditional probabilities can help in choosing the large numbers of parameters of the model in order to obtain a stationary model. Explicit results are given for the No Isolated Bits constraint. Finally we present a variation of the encoding scheme of bitstuffing that is applicable to the class of checkerboard constrained fields. It is possible to calculate the entropy of the coding scheme thus obtaining lower bounds on the entropy of the fields considered. These lower bounds are very tight for the RunLength limited fields. Explicit bounds are given for the diamond constrained field as well.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  111 
ISBN (Print)  9788790974978 
Publication status  Published  Sep 2006 
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Dive into the research topics of 'Coding for Two Dimensional Constrained Fields'. Together they form a unique fingerprint.Projects
 1 Finished

Constrained Coding for 2D Systems
Vaarby, T. S., Forchhammer, S., Larsen, K. J., Jensen, O. R. & Johansen, P.
15/08/2002 → 25/09/2006
Project: PhD