On Autocorrelation Properties Of Binary And Quaternary Sequences

Pseudorandom sequences with good autocorrelation play an important role in many fields, such as software testing systems, wireless communication systems, radar systems and stream ciphers. Such sequences are required to be easily distinguished from their shifted versions, that is, to have low nontrivial autocorrelation values. Due to the usefulness of pseudorandom sequences in the communication systems with binary and quaternary modulations, the binary and quaternary sequences have been paid more attentions in the sequence design. This dissertation investigates the properties and constructions of binary and quaternary sequences which are based on the interleaved structure and Gray mapping. The main results as follows:(1) This dissertation constructs a new class of quaternary sequences with period 4N, which generalizes the method based on the interleaved structure and Gray mapping proposed by Tang and Ding. It is shown that this kind of sequences are almost balanced and have good autocorrelation value. Then, these constructed quaternary sequences are classified and discussed via some different parameters, and we show that these sequences are equivalent.(2) This dissertation proposes two class of permutation methods according to the properties of balanced quaternary sequences and inverse Gray mapping. A balanced quaternary sequence can be obtained by another one through the first permutation method, and they have the same autocorrelation. Similarly, we can obtain four quaternary sequences from one quaternary sequence, and the sequences have the same real parts and the converse imaginary parts in the autocorrelation value. Then, the two permutation methods are analyzed and demonstrated. Last, the autocorrelation value of an arbitrary balanced quaternary sequences with long period are verified.(3) The detailed analysis of quaternary sequences with good autocorrelation is given, these sequences are generated by the different constructions, one was proposed by Jang and the other was proposed by Tang and Ding. We show that the two quaternary sequences sets are the same through these constructions which both used m-sequences set with period 12n-and found the intersection of the quaternary sets.(4) A new class of quaternary sequences is found by the construction of quaternary sequences which was proposed by Xiaohu Tang and C unsheng Ding. The autocorrelation of these new quaternary sequences is determined by relevant parameters. Additionally, the relationship between the parameter and the autocorrelation is given. In the end, simulation experiments explain that the autocorrelation values are correct.