A Multilevel Jacket Sequence Generation
6
조회
0
다운로드
0
인용
0
참고문헌
초록
The Jacket matrix is based on the Walsh-Hadamard matrix and an extension of the Center Weighted Hadamarad matrix[9]. While the elements of Walsh-Hadamard matrix are +1 or -1, those of Jacket matrix are ±1 and ±ω, which is ±j and ±2n. In this paper, a multilevel Jacket sequence generation method is proposed. The Jacket sequence is generated by the AND operations Exclusive-OR between the binary indices bits of row and column. The Jacket matrix is able to be weighted on the center of Hadamard matrix so that it should have the multiphase in complex domain and it consists of sign part and weight part. The main idea of this paper is how to assign the weight on the matrix and how to express it in general equation. It can be represented in binary index bits. The weight is imposed on the element only when the product of each Exclusive-OR operations of significant upper two binary index bits of a row and column is 1. Each part of the Jacket matrix can be represented by Jacket sequence using row and column binary index bits. This algorithm is simple and so can be easily implemented via the Karnaugh map of binary index bits of the Jacket matrix and its Exclusive-OR operations. It can be applied to the information hiding of using polynomial Jacket transform, the information theory, and complex spreading Jacket QPSK modulation for WCDMA.
Abstract
The Jacket matrix is based on the Walsh-Hadamard matrix and an extension of the Center Weighted Hadamarad matrix[9]. While the elements of Walsh-Hadamard matrix are +1 or -1, those of Jacket matrix are ±1 and ±ω, which is ±j and ±2n. In this paper, a multilevel Jacket sequence generation method is proposed. The Jacket sequence is generated by the AND operations Exclusive-OR between the binary indices bits of row and column. The Jacket matrix is able to be weighted on the center of Hadamard matrix so that it should have the multiphase in complex domain and it consists of sign part and weight part. The main idea of this paper is how to assign the weight on the matrix and how to express it in general equation. It can be represented in binary index bits. The weight is imposed on the element only when the product of each Exclusive-OR operations of significant upper two binary index bits of a row and column is 1. Each part of the Jacket matrix can be represented by Jacket sequence using row and column binary index bits. This algorithm is simple and so can be easily implemented via the Karnaugh map of binary index bits of the Jacket matrix and its Exclusive-OR operations. It can be applied to the information hiding of using polynomial Jacket transform, the information theory, and complex spreading Jacket QPSK modulation for WCDMA.