Bent functions and codes with low peak-to-average power ratio for multi-code CDMA

Authors:
Jianqin Zhou;Wai Ho Mow;Xiaoping Dai
Affiliations:
Department of Computer Science, Anhui University of Technology, Ma'anshan, China;Dept. of Electrical & Electronic Engineering, Hong Kong Univ. of Science and Technology, Hong Kong;Department of Computer Science, Anhui University of Technology, Ma'anshan, China
Venue:
AAECC'07 Proceedings of the 17th international conference on Applied algebra, algebraic algorithms and error-correcting codes
Year:
2007

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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.