Secure Channel Coding Schemes based on Algebraic-Geometric Codes over Hermitian Curves.

Algebraic-Geometric (AG) codes are new paradigm in coding theory with promising performance improvements and diverse applications in point to point communications services and system security. AG codes offer several advantages over state-of-the art Reed-Solomon (RS) codes. Algebraic-Geometric Codes are proposed and implemented in this paper. The design, construction and implementation are investigated and a software platform has been developed. Simulation results are presented for the first time showing significant performance improvements of AG codes over RS codes using different modulation schemes. The superiority in error correcting and security of AG codes over RS codes has been demonstrated clearly when Rayleigh fading channel is used. Also the results show an obvious improvement when using higher modulation schemes, namely 16QAM and 64QAM.