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In orthogonal frequency division multiplexing (OFDM) systems, for every block of K data samples, an overhead of L samples of cyclic prefix (CP) or zero padding (ZP) is added to combat frequency selective channels. The code rate, which is defined as the ratio K/(K+L), is a measure of the efficiency of transmitting user information. In this paper, a new system is proposed to increase the code rate without increasing the number of subcarriers and without increasing the bandwidth. The proposed system considers appending the L zeros (ZP) once for every P blocks of data samples, which would increase the code rate to PK/(PK+L). It is assumed that the channel is not varying over the transmission of P consecutive data blocks. In order to recover the P data blocks in a computationally efficient manner, an interleaving scheme is proposed, and the proposed system is called the interleaved OFDM (IOFDM) system. Various issues such as computational complexity, peak-to-average power ratio (PAPR), and the effect of synchronization errors on the performance of the IOFDM system are also presented. Based on a numerical simulation study, the average bit-error-rate (BER) performance of the IOFDM system is shown to be very close to that of the OFDM system for a moderate increase in computational complexity and delay.