Construction and performance of algebraic–geometric codes over AWGN and fading channels

Abstract

Algebraic geometry is a branch of mathematics with many applications such as statistics, computer science and economics. It can also be applied to coding theory to construct nonbinary block codes from curves with impressive parameters e.g. large code lengths, high code rates and large minimum distances. The design and construction of algebraic–geometric codes is described, and the performance evaluated over the additive white gaussian noise (AWGN) and Rayleigh fading channels and make comparisons with similar Reed–Solomon codes. Simulation results show that algebraic–geometric codes constructed from hermitian curves (hermitian codes) outperform Reed–Solomon codes of similar code rate and defined over the same finite field and show that hermitian codes would be suitable for a mobile radio environment.