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On the existence and construction of good codes with low peak-to-average power ratios

Publication ,  Journal Article
Paterson, KG; Tarokh, V
Published in: HP Laboratories Technical Report
April 1, 1999

The first lower bound on the peak-to-average power ratio (PAPR) of a constant energy code of a given length n, minimum Euclidean distance and rate is established. Conversely, using a non-constructive Varshamov-Gilbert 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 error-correcting 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 non-binary analogues. Some open problems are identified.

Duke Scholars

Published In

HP Laboratories Technical Report

Publication Date

April 1, 1999

Issue

51
 

Citation

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MLA
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Paterson, K. G., & Tarokh, V. (1999). On the existence and construction of good codes with low peak-to-average power ratios. HP Laboratories Technical Report, (51).
Paterson, K. G., and V. Tarokh. “On the existence and construction of good codes with low peak-to-average power ratios.” HP Laboratories Technical Report, no. 51 (April 1, 1999).
Paterson KG, Tarokh V. On the existence and construction of good codes with low peak-to-average power ratios. HP Laboratories Technical Report. 1999 Apr 1;(51).
Paterson, K. G., and V. Tarokh. “On the existence and construction of good codes with low peak-to-average power ratios.” HP Laboratories Technical Report, no. 51, Apr. 1999.
Paterson KG, Tarokh V. On the existence and construction of good codes with low peak-to-average power ratios. HP Laboratories Technical Report. 1999 Apr 1;(51).

Published In

HP Laboratories Technical Report

Publication Date

April 1, 1999

Issue

51