NDLI: Algebraic list-decoding of subspace codes with multiplicities

Content Provider	IEEE Xplore Digital Library
Author	Mahdavifar, H. Vardy, A.
Copyright Year	2011
Description	Author affiliation: University of California San Diego, La Jolla, CA 92093, USA (Mahdavifar, H.; Vardy, A.)
Abstract	Koetter and Kschischang introduced subspace codes in order to correct errors and erasures for randomized network coding, in the case where network topology is unknown (the noncoherent case). The codewords are vector subspaces of a fixed ambient space; thus codes for this model are collections of such subspaces. Koetter and Kschis-chang constructed a remarkable family of codes similar to Reed-Solomon codes in that codewords are obtained by evaluating certain (linearized) polynomials. In a previous work, we introduced a new family of sub-space codes based upon Koetter-Kschichang construction wich are efficiently list-decodable. By that we could achieve a better decoding radius at low rates than Koetter-Kschischiang codes. In this paper, we consider the problem of list-decoding of sub-space codes with multiplicities. We first establish the notion of multiplicity for linearized polynomials in this context. Then we take advantage of enforcing multiple roots for the interpolation polynomial in order to achieve a better decoding radius. We are also able to list-decode at higher rates. The end result is the following: for any integers L and r, our list-L decoder with multiplicity r guarantees successful recovery of the message subspace provided that the normalized dimension of the error is at most 2(L+1)/r+1 − 1 − L(L+1)/r(r+1) $R^{∗}$ where $R^{∗}$ is the normalized packet rate. This improves the normalized decoding radius upon the previous results for a wide range of rates. The parameter r is independent of the code construction and can be chosen at the decoder in such a way that the decoding radius is maximized. As L tends to infinity, the decoding radius of our construction with appropriate choice of r approaches $1/R^{∗}$ − 1.
Starting Page	1430
Ending Page	1437
File Size	886479
Page Count	8
File Format	PDF
ISBN	9781457718175
e-ISBN	9781457718182
DOI	10.1109/Allerton.2011.6120336
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2011-09-28
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Reed-Solomon codes Interpolation Network coding Polynomials Vectors Encoding Decoding
Content Type	Text
Resource Type	Article

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