On universally decodable matrices for space–time coding |
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Authors: | Pascal O Vontobel Ashwin Ganesan |
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Institution: | (1) Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, CA 94304, USA;(2) ECE Department, University of Wisconsin-Madison, 1415 Engineering Drive Madison, Madison, WI 53706, USA;(3) EECS Dept., Massachusetts Institute of Technology, Cambridge, MA 02139, USA |
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Abstract: | The notion of universally decodable matrices (UDMs) was recently introduced by Tavildar and Viswanath while studying slow-fading channels. It turns out that the problem of constructing UDMs is tightly connected to the problem of constructing maximum-distance separable codes. In this paper, we first study the properties of UDMs in general and then we discuss an explicit construction of a class of UDMs, a construction which can be seen as an extension of Reed–Solomon codes. In fact, we show that this extension is, in a sense to be made more precise later on, unique. Moreover, the structure of this class of UDMs allows us to answer some open conjectures by Tavildar, Viswanath, and Doshi in the positive, and it also allows us to formulate an efficient decoding algorithm for this class of UDMs. It turns out that our construction yields a coding scheme that is essentially equivalent to a class of codes that was proposed by Rosenbloom and Tsfasman. Moreover, we point out connections to so-called repeated-root cyclic codes. |
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Keywords: | Universally decodable matrices Coding for slow-fading channels Rank condition Efficient decoding Rosenbloom-Tsfasman metric Reed– Solomon codes Repeated-root cyclic codes Hasse derivatives Newton interpolation Pascal’ s triangle |
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