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Recently orthogonal frequency division multiplexing (OFDM) has gained a lot of attention in mobile radio communications because of its ability to allow high data rate transmission in a severe frequency selective fading channel. Rate compatible punctured turbo coded hybrid ARQ (RCPT HARQ) has been found to give improved throughput performance in a DS-CDMA system. However the extent to which the RCPT HARQ improves the throughput performance of the OFDM system has not been fully understood. In this paper we evaluate by computer simulations the performance of the RCPT HARQ for the OFDM system. It is found that the type II RCPT HARQ has the highest throughput when minimum amount of redundancy bits are transmitted with each retransmission, typical case is when the puncturing period for the parity sequences is 8. It was found that the OFDM system with RCPT HARQ outperforms the DS-CDMA system with RCPT HARQ in a frequency selective channel.