HP Labs Technical Reports
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On the Existence and Construction Of Good Codes with Low PeaktoAverage Power Ratios
Paterson, Kenneth G.; Tarokh, Vahid
HPL199951
Keyword(s): OFDM; multicarrier; power; PAPR; PMPR; PMEPR; bounds; Varshamov; Gilbert; simplex code; dual BCH code; Kerdock code; DelsarteGoethals code; exponential sum; Lagrange interpolation; finite field; Galois ring
Abstract: The first lower bound on the peaktoaverage power ratio (PAPR) of a constant energy code of a given length n, minimum Euclidean distance and rate is established. Conversely, using a nonconstructive VarshamovGilbert style argument yields a lower bound on the achievable rate of a code of a given length, minimum Euclidean distance and maximum PAPR. The derivation of these bounds relies on a geometrical analysis of the PAPR of such a code. Further analysis shows that there exist asymptotically good codes whose PAPR is at most 8 log n. These bounds motivate the explicit construction of errorcorrecting codes with low PAPR. Bounds for exponential sums over Galois fields and rings are applied to obtain an upper bound of order (log n)2 on the PAPRs of a constructive class of codes the trace codes. This class includes the binary simplex code, duals of binary, primitive BCH codes and a variety of their nonbinary analogues. Some open problems are identified. Notes: Vahid Tarokh, AT & T Labs  Research , 180 Park Avenue, Florham Park, New Jersey 07932, USA
22 Pages
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