On the Existence and Construction Of Good Codes with Low

Paterson, Kenneth G. ; Tarokh, Vahid

HP Development Company

关键词: OFDM;    multicarrier;    power;    PAPR;    PMPR;    PMEPR;    bounds;    Varshamov;    Gilbert;    simplex code;    dual BCH code;    Kerdock code;    Delsarte-Goethals code;    exponential sum;    Lagrange interpolation;    finite field;    Galois ring;   

RP-ID  :  HPL-1999-51

学科分类：计算机科学（综合）

美国|英语

来源: HP Labs

【 摘 要 】

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. Notes: Vahid Tarokh, AT & T Labs - Research , 180 Park Avenue, Florham Park, New Jersey 07932, USA 22 Pages