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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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 60; no. 1; pp. 271 - 281
Main Author: Schwartz, Moshe
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.01.2014
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2286616