This study will present the design, construction and implementation of Algebraic Geometric Irregular Block Turbo Codes (AGIBTCs). Furthermore, we will evaluate its performance over fast fading channels using different modulation schemes (BPSK, QPSK, 16QAM and 64QAM). The idea behind the design of AGIBTC is to overcome the high system complexity of Algebraic Geometric Block Turbo Codes (AGBTCs) while maintaining a high Bit-Error Rate (BER) performance. This design is inspired by the idea of unequal protection of information symbols which is the core of IBTCs. Our experiments conducted over the worst case of fading channels which is the fast fading channels; and this is done in order to show the magnitude of gain in BER or the reduction in system complexity that can be achieved by this design. Our experiments shows that despite a very slight negative gain over BPSK and QPSK modulation schemes the system complexity is significantly reduced. However, when applying higher modulation schemes a gain in both BER and system complexity are achieved.