On Locally Invertible Encoders and Multidimensional Convolutional Codes

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dc.contributor.advisor Dr. Mladen A. Vouk, Committee Co-Chair en_US
dc.contributor.advisor Dr. Donald L. Bitzer, Committee Co-Chair en_US
dc.contributor.advisor Dr. Brian L. Hughes, Committee Member en_US
dc.contributor.advisor Dr. Alexandra Duel-Hallen, Committee Member en_US
dc.contributor.advisor Dr. Ernest Stitzinger, Committee Member en_US
dc.contributor.author Lobo, Ruben Gerald en_US
dc.date.accessioned 2010-04-02T18:30:12Z
dc.date.available 2010-04-02T18:30:12Z
dc.date.issued 2006-08-10 en_US
dc.identifier.other etd-06252006-221507 en_US
dc.identifier.uri http://www.lib.ncsu.edu/resolver/1840.16/3451
dc.description.abstract Multidimensional (m-D) convolutional codes generalize the well known notion of a 1-D convolutional code defined over a univariate polynomial ring with coefficients in a finite field to multivariate polynomial rings. The more complicated structure of a multivariate polynomial ring when compared to a univariate one, however, makes the generalization nontrivial. While 1-D convolutional codes have been thoroughly understood and have wide applications in communication systems, the theory of m-D convolutional codes is still in its infancy, and these codes lack unified notation and practical implementation. This dissertation develops a sequence space approach for realizing m-D convolutional codes. While most of the existing research is focused on algebraic aspects, fundamental issues regarding practical implementation that are well developed and fairly straightforward in the 1-D case have remained undefined for m-D convolutional codes. In this dissertation we address some of these issues. We define a new notion of sequence space ordering and show that certain multivariate polynomial matrices which we call as locally invertible encoders, when transformed to the sequence space domain, have an invertible subsequence map between their input and output sequences. This subsequence map has a well defined structure that allows for the explicit construction of locally invertible encoders by performing elementary operations on the ground field without the use of any polynomial operations. We use the invertible subsequence map to introduce a novel method to encode and invert multidimensional sequences. We show that locally invertible encoders have good structural properties which make them a natural choice to generate multidimensional convolutional codes. en_US
dc.rights I hereby certify that, if appropriate, I have obtained and attached hereto a written permission statement from the owner(s) of each third party copyrighted matter to be included in my thesis, dissertation, or project report, allowing distribution as specified below. I certify that the version I submitted is the same as that approved by my advisory committee. I hereby grant to NC State University or its agents the non-exclusive license to archive and make accessible, under the conditions specified below, my thesis, dissertation, or project report in whole or in part in all forms of media, now or hereafter known. I retain all other ownership rights to the copyright of the thesis, dissertation or project report. I also retain the right to use in future works (such as articles or books) all or part of this thesis, dissertation, or project report. en_US
dc.subject multivariate polynomial matrix inverse en_US
dc.subject m-D convolutional codes en_US
dc.subject error control codes en_US
dc.subject locally invertible encoders en_US
dc.subject coding theory en_US
dc.title On Locally Invertible Encoders and Multidimensional Convolutional Codes en_US
dc.degree.name PhD en_US
dc.degree.level dissertation en_US
dc.degree.discipline Computer Engineering en_US

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