Abstract
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 2m for both even m as well as odd m.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
Paterson, K.G.: Generalised Reed-Muller Codes and Power Control in OFDM Modulation. IEEE Trans. Inform. Theory 46, 104–120 (2000)
Paterson, K.G., Jones, A.E.: Effcient Decoding Algorithms for Generalised Reed-Muller Codes. IEEE Trans. Commun. 48(8), 1272–1285 (2000)
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)
Qu, C., Seberry, J., Pieprzyk, J.: Homogeneous Bent Functions. Discrete Applied Mathematics 102, 133–139 (2000)
Rothaus, O.S.: On ”Bent” Functions. J. Combin. Theory Ser.A 20, 300–305 (1976)
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)
Wada, T.: Characteristic of Bit Sequences Applicable to Constant Amplitude Orthogonal Multicode Systems. IEICE Trans. Fundamentals E83-A(11), 2160–2164 (2000)
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)
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)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhou, J., Mow, W.H., Dai, X. (2007). Bent Functions and Codes with Low Peak-to-Average Power Ratio for Multi-Code CDMA. In: Boztaş, S., Lu, HF.(. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 2007. Lecture Notes in Computer Science, vol 4851. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77224-8_10
Download citation
DOI: https://doi.org/10.1007/978-3-540-77224-8_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77223-1
Online ISBN: 978-3-540-77224-8
eBook Packages: Computer ScienceComputer Science (R0)