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

Authors

James A. Davis, University of RichmondFollow
Jonathan Jedwab

DOI

10.1109/18.796380

Abstract

We present a range of coding schemes for OFDM transmission using binary, quaternary, octary, and higher order modulation that give high code rates for moderate numbers of carriers. 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 unrecognized connection between Golay complementary sequences and second-order Reed–Muller codes over alphabets ℤ_2^h. 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.

Document Type

Article

Publication Date

11-1999

Publisher Statement

Copyright © 1999, IEEE Information Theory Society. This article first appeared in IEEE Transactions on Information Theory: 45:7 (1999), 2397-2417.

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Recommended Citation

Davis, James A., and Jonathan Jedwab. "Peak-to-Mean Power Control in OFDM, Golay Complementary Sequences, and Reed–Muller Codes." IEEE Transactions on Information Theory 45, no. 7 (November 1999): 2397-417. doi: 10.1109/18.796380.