Iterative chase decoding of algebraic geometric codes

Abstract

This thesis presents an iterative decoding algorithm for algebraic geometric codes. We show here that the product codes whose component codes are non-binary one-point algebraic geometric codes over Klein quartic curve can achieve good BER performance in both AWGN channel and Rayleigh fading channel. Such codes are also called block turbo codes. In the construction of the product codes, both bit concatenation and symbol concatenation are used. All the product codes are represented in binary form. The Chase decoder with an inner hard-decision decoder using parallel Berlekamp-Massey algorithm is used as the soft-input soft-output decoder of the iterative decoding scheme. We proposed a codeword validation step in the SISO decoder to mitigate the restriction of the PBMA which decodes with respect to symbols.