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Complementary Sets, Generalized Reed–Muller Codes, and Power Control for OFDM

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1 Author(s)
Schmidt, K. ; Commun. Lab., Dresden Univ. of Technol.

The use of error-correcting codes for tight control of the peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency-division multiplexing (OFDM) transmission is considered in this correspondence. By generalizing a result by Paterson, it is shown that each q-phase (q is even) sequence of length 2m lies in a complementary set of size 2k+1, where k is a nonnegative integer that can be easily determined from the generalized Boolean function associated with the sequence. For small k this result provides a reasonably tight bound for the PMEPR of q-phase sequences of length 2 m. A new 2h-ary generalization of the classical Reed-Muller code is then used together with the result on complementary sets to derive flexible OFDM coding schemes with low PMEPR. These codes include the codes developed by Davis and Jedwab as a special case. In certain situations the codes in the present correspondence are similar to Paterson's code constructions and often outperform them

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Information Theory, IEEE Transactions on  (Volume:53 ,  Issue: 2 )