Multidimensional Quasi-Cyclic and Convolutional Codes
نویسندگان
چکیده
منابع مشابه
Quasi-cyclic unit memory convolutional codes
Unit memory convolutional codes with generator matrices, which are composed of circulant suhmatrices, are introduced. This structure facilitates the analysis as well as an efficient search for good codes. Equivalences among such codes and consider some of the basic structural properties are discussed. In particular, catastrophic encoders and minimal encoders are characterized and dual codes tre...
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Acknowledgements I would like to thank many people who helped and encouraged me with this work. My advisor, Joachim Rosenthal, worked with me long and patiently so that I could produce this dissertation. My committee members, Heide Gl using-L uerren, Alan Howard, and Juan Migliore, made many suggestions that have improved this work greatly. My academic \siblings", Brian Allen, Roxana Smarandach...
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Let R = Zq + uZq, where q = p and u = 0. In this paper, some structural properties of cyclic codes and quasi-cyclic (QC) codes over the ring R are considered. A QC code of length ln with index l over R is viewed both as in the conventional row circulant form and also as an R[x]/(x − 1)-submodule of GR(R, l)[x]/(x − 1), where GR(R, l) is the Galois extension ring of degree l over R. A necessary ...
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Multidimensional convolutional codes arise as a generalization of “classical” onedimensional codes. We will introduce m-dimensional convolutional codes of length n as submodules of Dn where D is the polynomial ring in m variables over a finite field. Besides their coding theoretic significance, they can also be regarded as the annihilating modules of systems of partial difference equations, the...
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ژورنال
عنوان ژورنال: IEEE Transactions on Information Theory
سال: 2016
ISSN: 0018-9448,1557-9654
DOI: 10.1109/tit.2016.2616467