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Reed-Muller Codes for Peak Power Control in Multicarrier CDMA

Reed-Muller codes are studied for peak power control in multicarrier code-division multiple access (MC-CDMA) communication systems. In a coded MC-CDMA system, the information data multiplexed from users is encoded by a Reed-Muller subcode and the codeword is fully-loaded to Walsh-Hadamard spreading sequences. The polynomial representation of a coded MC-CDMA signal is established for theoretical analysis of the peak-to-average power ratio (PAPR). The Reed-Muller subcodes are defined in a recursive way by the Boolean functions providing the transmitted MC-CDMA signals with the bounded PAPR as well as the error correction capability. A connection between the code rates and the maximum PAPR is theoretically investigated in the coded MC-CDMA. Simulation results present the statistical evidence that the PAPR of the coded MC-CDMA signal is not only theoretically bounded, but also statistically reduced. In particular, the coded MC-CDMA solves the major PAPR problem of uncoded MC-CDMA by dramatically reducing its PAPR for the small number of users. Finally, the theoretical and statistical studies show that the Reed-Muller subcodes are effective coding schemes for peak power control in MC-CDMA with small and moderate numbers of users, subcarriers, and spreading factors.