  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.
