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Peak-to-Mean Power Control in OFDM, Golay Complementary Sequences and Reed-Muller Codes

Davis, James A.; Jedwab, Jonathan


Keyword(s): power; envelope; OFDM; Golay; complementary; sequence; Reed-Muller; code

Abstract: We present a range of coding schemes for OFDM transmission at high code rates using binary, quaternary, octary and higher-order modulation. These schemes have tightly bounded peak-to-mean envelope power ratio (PMEPR) and simultaneously have good error correction capability. The key theoretical result is a previously unrecognised connection between Golay complementary sequences and second-order Reed-Muller codes over alphabets Z2h. We obtain additional flexibility in trading off code rate, PMEPR and error correction capability by partitioning the second-order Reed-Muller code into cosets such that codewords with large values of PMEPR are isolated. For all the proposed schemes, we show that encoding is straightforward and give an efficient decoding algorithm involving multiple fast Hadamard transforms. Since the coding schemes are all based on the same formal generator matrix, we can deal adaptively with varying channel constraints and evolving system requirements.

26 Pages

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