期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 46, 期 1, 页码 104-120出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/18.817512
关键词
code; complementary; encoding; Golay; multicarrier; OFDM; PMEPR; power; Reed-Muller; sequence; set
Controlling the peak-to-mean envelope power ratio (PMEPR) of orthogonal frequency-division multiplexed (OFDM) transmissions is a notoriously difficult problem, though one which is of vital importance for the practical application of OFDM in low-cost applications. The utility of Golay complementary sequences in solving this problem has been recognized for some time. In this paper, a powerful theory linking Golay complementary sets of polyphase sequences and Reed-Muller codes is developed, Our main result shows that any second-order coset of a q-ary generalization of the first order Reed-Muller code can be partitioned into Golay complementary sets whose size depends only on a single parameter that is easily computed from a graph associated with the coset, As a first consequence, recent results of Davis and Jedwab on Golay pairs, as well as earlier constructions of Golay, Budisin and Sivaswamy are shown to arise as special cases of a unified theory for Golay complementary sets, As a second consequence, the main result directly yields bounds on the PMEPR's of codes formed from selected cosets of the generalized first order Reed-Muller code. These codes enjoy efficient encoding, good error-correcting capability, and tightly controlled PMEPR, and significantly extend the range of coding options for applications of OFDM using small numbers of carriers.
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