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Sequences for OFDM and Multi-Code CDMA : Two Problems in Algebraic Coding Theory

Paterson, Kenneth G.

HPL-2001-146

Keyword(s): OFDM; CDMA; PAPR; sequences; Golay; Reed-Muller

Abstract: We study the peak-to-average power ratio (PAPR) problem for two different kinds of communications systems, Orthogonal Frequency Division Multiplexing (OFDM) and Multi-Code Code-Division Multiple Access (MC-CDMA). We describe a common coding theoretic approach to reducing the PAPR of both kinds of transmissions. In both cases, the classical Reed- Muller codes turn out to play a critical role. There is an intimate connection between Reed-Muller codes and Golay complementary sequences which can be exploited to produce codes suitable for OFDM. For MC- CDMA, it turns out that bent functions lead to transmissions with ideal power characteristics. In this way, the problem of finding good codes for OFDM and MC-CDMA can be closely related to some old and new problems in algebraic coding theory and sequence design.

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