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

IEEE Transactions on Information Theory

Volumn 46, Issue 6, 2000, Pages 1974-1987

  Paterson, Kenneth G ^a,b   Tarokh, Vahid ^a,b,c  

^a IEEE

^b HEWLETT PACKARD LABORATORIES   (United Kingdom)

^c AT AND T LABS RESEARCH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CARRIER COMMUNICATION; CODES (SYMBOLS); COMPUTATIONAL COMPLEXITY; ERROR CORRECTION; FREQUENCY DIVISION MULTIPLEXING; INTEGER PROGRAMMING; MULTICARRIER MODULATION;

BOSE-CHAUDHURI-HOCQUENGHEM (BCH) CODE; DELSARTE-GOETHALS CODE; GALOIS RING; KERDOCK CODE; LAGRANGE INTERPOLATION; PEAK-TO-AVERAGE POWER RATIO (PAPR);

DIGITAL SIGNAL PROCESSING;

EID: 0034270963     PISSN: 00189448     EISSN: None     Source Type: Journal    
DOI: 10.1109/18.868473     Document Type: Article

References (47)

1. M. Alard and R. Lasalle, Principles of modulation and channel coding for digital broadcasting for mobile receivers, EBU Rev., vol. 224, pp. 47-69, Aug. 1987.
2. J. Beck, Flat polynomials on the unit circle-Note on a problem of Littlewood, Bull. London Math. Soc., vol. 23, pp. 269-277, 1991.
3. P. A. Bello, Selective fading limitations of the Kathryn modem and some system design considerations, IEEE Trans. Commun. Technol, vol. COM-13, pp. 320-333, Sept. 1965.
4. J. A. C. Bingham, Multicarrier modulation for data transmission: An idea whose time has come, IEEE Commun. Mag., vol. 28, pp. 5-14, May 1990.
5. R. W. Chang, Synthesis of band-limited orthogonal signals for multichannel data transmission, Bell Syst. Tech. J., vol. 45, pp. 1775-1796, Dec. 1966.
6. R. W. Chang and R. A. Gibbey, A theoretical study of performance of an orthogonal multiplexing data transmission scheme, IEEE Trans. Commun. Technol., vol. COM-16, pp. 529-540, Aug. 1968.
7. P. S. Chow, J. M. Cioffi, and J. A. C. Bingham, DMT-based ADSL: Concept, architecture, and performance," in IEE Coll. High Speed Access Technology and Services, Including Video-on-Demand, Oct. 1-6, 1994, p. 3.
8. L. J. Cimini Jr., Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing, IEEE Trans. Commun., vol. COM-33, pp. 665-675, July 1985.
9. J. A. Davis and J. Jedwab, Peak-to-mean power control and error correction for OFDM transmission using Golay sequences and Reed-Muller codes, Electron. Lett., vol. 33, pp. 267-268, 1997.
10. _, Peak-to-mean power control in OFDM, Golay complementary sequences and Reed-Muller codes, IEEE Trans. Inform. Theory, vol. 45, pp. 2397-2417, Nov. 1999.
11. M. L. Doelz, E. T. Heald, and D. L. Martin, Binary data transmission techniques for linear systems, Proc. IRE, vol. 45, pp. 656-661, May 1957.
12. M. Friese, Multicarrier modulation with low peak-to-mean average power ratio, Electron. Lett., vol. 32, pp. 713-714, 1996.
13. A. Gersho, B. Gopinath, and A. M. Odlyzko, Coefficient inaccuracy in transversal filtering, Bell Syst. Tech. J., vol. 58, pp. 2301-2316, 1979.
14. A. J. Grant and R. D. J. van Nee, Efficient maximum-likelihood decoding of Q-ary modulated Reed-Muller codes, IEEE Commun. Lett., vol. 2, pp. 134-136, 1998.
15. A. R. Hammons Jr., P. V. Kumar, A. R. Calderbank, N. J. A. Sloane, and P. Sole, The Z4-linearity of Kerdock, Preparata, Goethals, and related codes, IEEE Trans. Inform. Theory, vol. 40, pp. 301-319, Mar. 1994.
16. T. Helleseth, P. V. Kumar, O. Moreno, and A. G. Shanbhag, Improved estimates via exponential sums for the minimum distance of Z4-linear trace codes, IEEE Trans. Inform. Theory, vol. 42, pp. 1212-1216, July 1996.
17. T. F. Ho and V. K. Wei, Synthesis of low-crest waveforms for multicarrier CDMA systems," in Proc. IEEE GLOBECOMM, 1995, pp. 131-135.
18. J. Jedwab, Comment: M-sequences for OFDM peak-to-average power ratio reduction and error correction, Electron. Lett., vol. 33, pp. 1293-1294, 1997.
19. A. E. Jones, T. A. Wilkinson, and S. K. Barton, Block coding scheme for reduction of peak to mean envelope power ratio of multicarrier transmission schemes, Electron. Lett., vol. 30, pp. 2098-2099, 1994.
20. A. E. Jones and T. A. Wilkinson, Combined coding error control and increased robustness to system nonlinearities in OFDM," in Proc. IEEE 46th Vehicular Technology Conf., Atlanta, GA, 1996, pp. 904-908.
21. P. V. Kumar, T. Helleseth, and A. R. Calderbank, An upper bound for Weil exponential sums over Galois rings and applications, IEEE Trans. Inform. Theory, vol. 41, pp. 456168, 1995.
22. J. Lahtonen, On the odd and aperiodic correlation properties of the Kasami sequences, IEEE Trans. Inform. Theory, vol. 41, pp. 1506-1508, Sept. 1995.
23. R. Lidl and H. Niederreiter, Finite fields," in Encyclopedia of Mathematics and Its Applications, 2nd ed. Cambridge, U.K.: Cambridge Univ. Press, 1997, vol. 20.
24. X. Li and L. J. Cimini Jr., Effects of clipping and filtering on the performance of OFDM," in Proc. IEEE 47th Vehicular Technology Conf., Phoenix, 1997, pp. 1634-1638.
25. X. Li and J. A. Ritcey, M-sequences for OFDM peak-to-average power ratio reduction and error correction, Electron. Lett., vol. 33, pp. 554-555, 1997.
26. F. J. Mac Williams and N. J. A. Sloane, The Theory of Error-Correcting Codes, 2nd ed. Amsterdam, The Netherlands: North Holland, 1986.
27. O. Moreno and C. J. Moreno, The MacWilliams-Sloane conjecture on the tightness of the Carlitz-Uchiyama bound and the weights of duals of BCH codes, IEEE Trans. Inform. Theory, vol. 40, pp. 1894-1907, Nov. 1994.
28. S. H. Müller, R. W. Bäuml, R. F. H. Fischer, and J. B. Huber, OFDM with reduced peak-to-average power ratio by multiple signal representation," A. Télécommun., vol. 52, pp. 58-67, 1997.
29. R. D. J. van Nee, OFDM codes for peak-to-average power reduction and error correction," in Proc. IEEE GLOBECOM, London, U.K., 1996, pp. 740-744.
30. H. Ochiai and H. Imai, Block coding scheme based on complementary sequences for multicarrier signals, IEICE Trans. Fundamentals, pp. 2136-2143, 1997.
31. R. O'NeillandL. B. Lopes, Envelope variations and spectral splatter in clipped multicarrier signals," in Proc. PIMRC'95, Sept. 1995, pp. 71-75.
32. K. G. Paterson, Generalized Reed-Muller codes and power control in OFDM modulation, IEEE Trans. Inform. Theory, vol. 46, pp. 104-120, Jan. 2000.
33. K. G. Paterson and A. E. Jones, Efficient decoding algorithms for generalized Reed-Muller codes, IEEE Trans. Commun., vol. 48, pp. 1272-1285, Aug. 2000.
34. P. Piret, Bounds for codes over the unit circle, IEEE Trans. Inform. Theory, vol. IT-32, pp. 760-767, Nov. 1986.
35. G. C. Porter, Error distribution and diversity performance of a frequency-differential PSK HE modem, IEEE Trans. Commun. Technol., vol. COM-16, pp. 567-575, 1968.
36. B. R. Saltzberg, Performance of an efficient data transmission system, IEEE Trans. Commun. Technol, vol. COM-15, pp. 805-813, 1967.
37. J. Salz and S. B. Weinstein, Fourier transform communication system," in P roc. ACM Symp. Probl. Optimiz. Data Commun. Syst., Pine Mountain, GA, Oct. 1969, pp. 99-128.
38. D. V. Sarwate, An upper bound on the aperiodic autocorrelation function for a maximal-length sequence, IEEE Trans. Inform. Theory, vol. IT-30, pp. 685-687, July 1984.
39. W. Schmidt, Equations Over Finite Fields-An Elementary Approach. Berlin, Germany: Springer, 1976.
40. A. G. Shanbhag, P. V. Kumar, and T. Helleseth, Upper bound for a hybrid sum over Galois rings with applications to aperiodic correlation for some g-ary sequences, IEEE Trans. Inform. Theory, vol. 42, pp. 250-254, Jan. 1996.
41. C. E. Shannon, Probability of error for optimal codes in a Gaussian channel," in Claude Shannon Collected Papers. Piscataway, NJ: IEEE Press, 1993, pp. 279-324.
42. S. Shepherd, J. Orriss, and S. Barton, Asymptotic limits in peak envelope power reduction by redundant coding in orthogonal frequency-division multiplex modulation, IEEE Trans. Commun., vol. 46, pp. 5-10, Jan. 1998.
43. V. Tarokh and H. Jafarkhani, On reducing the peak to average power ratio in multicarrier communications, IEEE Trans. Commun., vol. 48, pp. 374, Jan. 2000.
44. S. B. Weinstein and P. M. Ebert, Data transmission by frequency-division multiplexing using the discrete Fourier transform, IEEE Trans. Commun. Technol., vol. COM-19, pp. 628-634, 1971.
45. T. A. Wilkinson and A. E. Jones, Minimization of the peak to mean envelope power ratio of multicarrier transmission schemes by block coding," in Proc. IEEE 45th Vehicular Technology Conf., Chicago, IL, July 1995, pp. 825-829.
46. D. Wulich, Reduction of peak-to-mean ratio of multicarrier modulation using cyclic coding, Electron. Lett., vol. 32, pp. 432133, 1996.
47. M. S. Zimmerman and A. L. Kirsch, The AN/GSC-10 (KATHRYN) variable rate data modem for HF radio, IEEE Trans. Commun. Technol., vol. COM-15, pp. 197-205, 1967.