Diversity-multiplexing Gain Tradeoff: a Tool in Algebra?

Details Diversity-multiplexing Gain Tradeoff: a Tool in Algebra? Diversity-multiplexing Gain Tradeoff: a Tool in Algebra?

2011-05-18

arxiv.org/abs/1105.3569v1

Computer Science

Information Theory

A preprint version of the paper submitted to 2011 IEEE Information Theory Workshop (ITW 2011), Paraty, Brazil

Scientific paper

Since the invention of space-time coding numerous algebraic methods have been applied in code design. In particular algebraic number theory and central simple algebras have been on the forefront of the research. In this paper we are turning the table and asking whether information theory can be used as a tool in algebra. We will first derive some corollaries from diversity-multiplexing gain (DMT) bounds by Zheng and Tse and later show how these results can be used to analyze the unit group of orders of certain division algebras. The authors do not claim that the algebraic results are new, but we do find that this interesting relation between algebra and information theory is quite surprising and worth pointing out.

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