Bent Functions and Codes with Low Peak-to-Average Power Ratio for Multi-Code CDMA

  • Jianqin Zhou
  • Wai Ho Mow
  • Xiaoping Dai
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4851)


In this paper, codes which reduce the peak-to-average power ratio (PAPR) in multi-code code division multiple access (MC-CDMA) communication systems are studied. It is known that using bent functions to define binary codewords gives constant amplitude signals. Based on the concept of quarter bent functions, a new inequality relating the minimum order of terms of a bent function and the maximum Walsh spectral magnitude is proved, and it facilitates the generalization of some known results. In particular, a new simple proof of the non-existence of the homogeneous bent functions of degree m in 2m boolean variables for m > 3 is obtained without invoking results from the difference set theory. We finally propose a new coding approach to achieve the constant amplitude transmission of codeword length 2 m for both even m as well as odd m.


CDMA multi-code Walsh-Hadamard transform PAPR bent function 


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  1. 1.
    Paterson, K.G.: On Codes with Low Peak-To-Average Power Ratio for Multi-Code CDMA. IEEE Trans. Inform. Theory 50(3), 550–559 (2004)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Paterson, K.G.: Generalised Reed-Muller Codes and Power Control in OFDM Modulation. IEEE Trans. Inform. Theory 46, 104–120 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Paterson, K.G., Jones, A.E.: Effcient Decoding Algorithms for Generalised Reed-Muller Codes. IEEE Trans. Commun. 48(8), 1272–1285 (2000)zbMATHCrossRefGoogle Scholar
  4. 4.
    Paterson, K.G., Tarokh, V.: On the Existence and Construction of Good Codes with Low Peak-To-Average Power Ratios. IEEE Trans. Inform. Theory 46(6), 1974–1987 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Qu, C., Seberry, J., Pieprzyk, J.: Homogeneous Bent Functions. Discrete Applied Mathematics 102, 133–139 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Rothaus, O.S.: On ”Bent” Functions. J. Combin. Theory Ser.A 20, 300–305 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Xia, T., Seberry, J., Pieprzyk, J., Charnes, C.: Homogeneous Bent Functions pf Degree n in 2n Variables Do Not Exist for n > 3. Discrete Applied Mathematics 142, 127–132 (2004)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Wada, T.: Characteristic of Bit Sequences Applicable to Constant Amplitude Orthogonal Multicode Systems. IEICE Trans. Fundamentals E83-A(11), 2160–2164 (2000)Google Scholar
  9. 9.
    Wada, T., Yamazato, M., Ogawa, A.: A Constant Amplitude Coding for Orthogonal Multi-Code CDMA Systems. IEICE Trans. Fundamentals E80-A(12), 2477–2484 (1997)Google Scholar
  10. 10.
    Wada, T., Yamazato, T., Katayama, M., Ogawa, A.: Error Correcting Capability of Constant Amplitude Coding for Orthogonal Multi-Code CDMA Systems. IEICE Trans. Fundamentals E81-A(10), 2166–2169 (1998)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jianqin Zhou
    • 1
  • Wai Ho Mow
    • 2
  • Xiaoping Dai
    • 1
  1. 1.Department of Computer Science, Anhui University of Technology, Ma’anshan, 243002China
  2. 2.Dept. of Electrical & Electronic Engineering, Hong Kong Univ. of Science and Technology, Clear Water BayHong Kong

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