High-rate codes with bounded PMEPR for BPSK and other symmetric constellations

In this letter, we consider the problem of constructing high-rate codes with low peak-to-mean-envelope power ratio (PMEPR) for multicarrier signals. Assuming coefficients of the multicarrier signal are chosen from a symmetric q-ary constellation, we construct codes with rate 1-(1/r)logq2 and PMEPR of less than crlogn for any r and n, where n is the number of subcarriers and c is a constant independent of n and r. The construction is based on dividing n subcarriers into n/r groups of r subcarriers and choosing a sign for each group to minimize the PMEPR. The signs are chosen using a variation of the algorithm proposed by the authors in previous papers. For large n, we can, in fact, construct a code with a rate of 1-O(1/logn) and PMEPR of less than clog2n. For binary phase-shift-keying-modulated signals, this partially solves the problem posed by Litsyn and implies a construction of 2n/2 codewords with PMEPR less than 2clogn

[1]  Babak Hassibi,et al.  Existence of codes with constant PMEPR and related design , 2004, IEEE Transactions on Signal Processing.

[2]  Simon Litsyn,et al.  A method to suppress high peaks in BPSK-modulated OFDM signal , 2004, IEEE Transactions on Communications.

[3]  Babak Hassibi,et al.  Peak to average power reduction using amplitude and sign adjustment , 2004, 2004 IEEE International Conference on Communications (IEEE Cat. No.04CH37577).

[4]  Babak Hassibi,et al.  On multicarrier signals where the PMEPR of a random codeword is asymptotically logn , 2004, IEEE Transactions on Information Theory.

[5]  M. Sharif,et al.  On the existence of codes with constant bounded PMEPR for multicarrier signals , 2003, IEEE International Symposium on Information Theory, 2003. Proceedings..

[6]  Babak Hassibi,et al.  A deterministic algorithm that achieves the PMEPR of c log n for multicarrier signals , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[7]  Holger Boche,et al.  Peak value estimation of bandlimited signals from their samples, noise enhancement, and a local characterization in the neighborhood of an extremum , 2003, IEEE Trans. Signal Process..

[8]  Holger Boche,et al.  Upper bounds on the statistical distribution of the crest-factor in OFDM transmission , 2003, IEEE Trans. Inf. Theory.

[9]  Hideki Ochiai,et al.  Performance of the deliberate clipping with adaptive symbol selection for strictly band-limited OFDM systems , 2000, IEEE Journal on Selected Areas in Communications.

[10]  J. Tellado,et al.  Multicarrier Modulation with Low Par: Applications to DSL and Wireless , 2000 .

[11]  K. Paterson,et al.  On the existence and construction of good codes with low peak-to-average power ratios , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[12]  Kenneth G. Paterson,et al.  Generalized Reed-Muller codes and power control in OFDM modulation , 1998, IEEE Trans. Inf. Theory.

[13]  Xiaodong Li,et al.  Effects of clipping and filtering on the performance of OFDM , 1998, IEEE Communications Letters.

[14]  J.B. Huber,et al.  A comparison of peak power reduction schemes for OFDM , 1997, GLOBECOM 97. IEEE Global Telecommunications Conference. Conference Record.

[15]  Xiaodong Li,et al.  Effects of clipping and filtering on the performance of OFDM , 1997, 1997 IEEE 47th Vehicular Technology Conference. Technology in Motion.

[16]  Karl Zeller,et al.  Schwankung von Polynomen zwischen Gitterpunkten , 1964 .

[17]  A. Barg,et al.  Algebraic coding theory and information theory : DIMACS workshop December 15-18, 2003 , 2005 .

[18]  D.L. Jones,et al.  Peak power reduction in OFDM and DMT via active channel modification , 1999, Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers (Cat. No.CH37020).