NDLI: Error-Correcting Codes in Projective Spaces Via Rank-Metric Codes and Ferrers Diagrams

Content Provider	IEEE Xplore Digital Library
Author	Etzion, T. Silberstein, N.
Copyright Year	1963
Abstract	Coding in the projective space has received recently a lot of attention due to its application in network coding. Reduced row echelon form of the linear subspaces and Ferrers diagram can play a key role for solving coding problems in the projective space. In this paper, we propose a method to design error-correcting codes in the projective space. We use a multilevel approach to design our codes. First, we select a constant-weight code. Each codeword defines a skeleton of a basis for a subspace in reduced row echelon form. This skeleton contains a Ferrers diagram on which we design a rank-metric code. Each such rank-metric code is lifted to a constant-dimension code. The union of these codes is our final constant-dimension code. In particular, the codes constructed recently by Koetter and Kschischang are a subset of our codes. The rank-metric codes used for this construction form a new class of rank-metric codes. We present a decoding algorithm to the constructed codes in the projective space. The efficiency of the decoding depends on the efficiency of the decoding for the constant-weight codes and the rank-metric codes. Finally, we use puncturing on our final constant-dimension codes to obtain large codes in the projective space which are not constant-dimension.
Sponsorship	IEEE Information Theory Society
Starting Page	2909
Ending Page	2919
Page Count	11
File Size	246860
File Format	PDF
ISSN	00189448
Volume Number	55
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Error correction codes Space technology Network coding Decoding Extraterrestrial measurements Skeleton Design methodology Galois fields Computer science reduced row echelon form Constant-dimension codes constant-weight codes Ferrers diagram identifying vector network coding projective space codes puncturing rank-metric codes
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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