Computer Science – Information Theory
Scientific paper
2011-11-27
Computer Science
Information Theory
A draft version of the paper submitted to Transactions on Information Theory. In this version Proposition 3.4 is corrected
Scientific paper
Since the invention of space-time coding numerous algebraic methods have been applied to code design. In particular algebraic number theory and central simple algebras have been at the forefront of the research. In the first part of the paper we will push this direction further and show how the error probability of algebraic codes is tied to some central aspects of algebraic number theory and central simple algebras. In particular we prove how the error probability of several algebraic codes is tied to the corresponding zeta functions and unit groups. In the second part of this paper we turn to study what information theory can say about algebra. We will first derive some corollaries from the diversity-multiplexing gain tradeoff (DMT) Zheng and Tse and later show how these results can be used to analyze the unit group of orders of certain division algebras.
Lu Hsiao-feng
Vehkalahti Roope
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