Algebraic Number Theory and Code Design for Rayleigh Fading Channels

Author(s): Frédérique Oggier;Emanuele Viterbo

Source:
    Journal:Foundations and Trends® in Communications and Information Theory
    ISSN Print:1567-2190,  ISSN Online:1567-2328
    Publisher:Now Publishers
    Volume 1 Number 3,

Document Type: Article
Pages: 84 (333-416)
DOI: 10.1561/0100000003

Abstract: Algebraic number theory is having an increasing impact in code design for many different coding applications, such as single antenna fading channels and more recently, MIMO systems. Extended work has been done on single antenna fading channels, and algebraic lattice codes have been proven to be an effective tool. The general framework has been settled in the last ten years and many explicit code constructions based on algebraic number theory are now available. The aim of this work is to provide both an overview on algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory. The basic facts of this mathematical field will be illustrated by many examples and by the use of a computer algebra freeware in order to make it more accessible to a large audience.

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