Gray Codes and Enumerative Coding for Vector Spaces

Gray codes for vector spaces are considered in two graphs: the Grassmann graph, and the projective-space graph, both of which have recently found applications in network coding. For the Grassmann graph, constructions of cyclic optimal codes are given for all parameters. As for the projective-space g...

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Vydáno v:	IEEE transactions on information theory Ročník 60; číslo 1; s. 271 - 281
Hlavní autor:	Schwartz, Moshe
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.01.2014 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Algebra Algorithm design and analysis Applied sciences Coding, codes Complexity theory Decoding Electrical engineering Encoding Enumerative coding Exact sciences and technology Grassmannian Gray codes Indexes Information theory Information, signal and communications theory projective-space graph Reflective binary codes Signal and communications theory Switching and signalling Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Vectors Performance evaluation Enumerative coding Cyclic code Packet switching Gray code Graph construction projective-space graph Grassmannian Decoding Algorithm Computational complexity Vector space Gray codes Network coding Optimal code Projective space
ISSN:	0018-9448, 1557-9654
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Abstract	Gray codes for vector spaces are considered in two graphs: the Grassmann graph, and the projective-space graph, both of which have recently found applications in network coding. For the Grassmann graph, constructions of cyclic optimal codes are given for all parameters. As for the projective-space graph, two constructions for specific parameters are provided, as well some nonexistence results. Furthermore, encoding and decoding algorithms are given for the Grassmannian Gray code, which induce an enumerative-coding scheme. The computational complexity of the algorithms is at least as low as known schemes, and for certain parameter ranges, the new scheme outperforms previously known ones.
AbstractList	Gray codes for vector spaces are considered in two graphs: the Grassmann graph, and the projective-space graph, both of which have recently found applications in network coding. For the Grassmann graph, constructions of cyclic optimal codes are given for all parameters. As for the projective-space graph, two constructions for specific parameters are provided, as well some nonexistence results. Furthermore, encoding and decoding algorithms are given for the Grassmannian Gray code, which induce an enumerative-coding scheme. The computational complexity of the algorithms is at least as low as known schemes, and for certain parameter ranges, the new scheme outperforms previously known ones. [PUBLICATION ABSTRACT] Gray codes for vector spaces are considered in two graphs: the Grassmann graph, and the projective-space graph, both of which have recently found applications in network coding. For the Grassmann graph, constructions of cyclic optimal codes are given for all parameters. As for the projective-space graph, two constructions for specific parameters are provided, as well some nonexistence results. Furthermore, encoding and decoding algorithms are given for the Grassmannian Gray code, which induce an enumerative-coding scheme. The computational complexity of the algorithms is at least as low as known schemes, and for certain parameter ranges, the new scheme outperforms previously known ones.
Author	Schwartz, Moshe
Author_xml	– sequence: 1 givenname: Moshe surname: Schwartz fullname: Schwartz, Moshe email: schwartz@ee.bgu.ac.il organization: Dept. of Electr. & Comput. Eng., Ben-Gurion Univ. of the Negev, Beer-Sheva, Israel
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Keywords	Performance evaluation Enumerative coding Cyclic code Packet switching Gray code Graph construction projective-space graph Grassmannian Decoding Algorithm Computational complexity Vector space Gray codes Network coding Optimal code Projective space
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SubjectTerms	Algebra Algorithm design and analysis Applied sciences Coding, codes Complexity theory Decoding Electrical engineering Encoding Enumerative coding Exact sciences and technology Grassmannian Gray codes Indexes Information theory Information, signal and communications theory projective-space graph Reflective binary codes Signal and communications theory Switching and signalling Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Vectors
Title	Gray Codes and Enumerative Coding for Vector Spaces
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