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In this paper, we present an unequal power allocation technique to increase the throughput of code-division multiple-access (CDMA) systems with chip-level interleavers. Performance is optimized, respectively, based on received and transmitted power allocation. Linear programming and power matching techniques are developed to provide solutions to systems with a very large number of users. Various numerical results are provided to demonstrate the efficiency of the proposed techniques and to examine the impact of system parameters, such as iteration number and interleaver length. We also show that with some very simple forward error correction codes, such as repetition codes or convolutional codes, the proposed scheme can achieve throughput reasonably close to that predicted by theoretical limit in multiple access channels.