A Unified Construction for Yielding Quaternary Sequences with Optimal Periodic Autocorrelation

Fanxin ZENG  Xiaoping ZENG  Zhenyu ZHANG  Guixin XUAN  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E96-A   No.7   pp.1593-1601
Publication Date: 2013/07/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E96.A.1593
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Information Theory
quaternary sequence,  balanced property,  autocorrelation,  interleaved sequence,  Gray mapping,  

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A unified construction for transforming binary sequences of balance or unbalance into quaternary sequences is presented. On the one hand, when optimal and balanced binary sequences with even period are employed, our construction is exactly the same Jang, et al.'s and Chung, et al.'s ones, which result in balanced quaternary sequences with optimal autocorrelation magnitude. On the other hand, when ideal and balanced binary sequences with odd period N are made use of, our construction produces new balanced quaternary sequences with optimal autocorrelation value (OAV), in which there are N distinct sequences in terms of cyclic shift equivalence, and includes Tang, et al.'s and Jang, et al.'s ones as special cases. In addition, when binary sequences without period 2n-1 or balance are employed, the transformation of Jang, et al.'s method is invalid, however, the proposed construction works very good. As a consequence, this unified construction allows us to construct optimal and balanced quaternary sequences from ideal/optimal balanced binary sequences with arbitrary period.