A Survey/Tutorial on Lattice Codes for Rayleigh Fading Channels

F. E. Oggier, E. Viterbo. ``Algebraic Number Theory and Code Design for Rayleigh Fading Channels", Foundations and Trends in Communications and Information Theory, December 2004. 
Algebraic number theory is gaining 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 the following work is both to provide a unified overview on algebraic lattice code designs for Rayleigh fading channels, as well as a tutorial introduction to algebraic number theory.