Title: Fast circulant block Jacket transform based on the Pauli matrices

Authors: Guibo Liu; Zhan Wang; Dayong Luo; Ying Guo; Moon Ho Lee

Addresses: School of Information Science and Engineering, Central South University, Changsha 410083, China ' School of Information Science and Engineering, Central South University, Changsha 410083, China ' School of Information Science and Engineering, Central South University, Changsha 410083, China ' School of Information Science and Engineering, Central South University, Changsha 410083, China ' Institute of Information and Communication, Chonbuk National University, Jeonju 561-756, South Korea

Abstract: Owing to its orthogonality, simplicity of the inversion and fast algorithms, Jacket transform generalising from the Hadamard transform has played important roles in signal and image processing, mobile communication for coding design, cryptography, etc. In this paper, inspired by the emerging block Jacket transform, a new class of circulant block Jacket matrices (CBJMs) are mathematically defined based on the circulant matrix theory. Then the existence conditions for the CBJMs with any size based on the Pauli matrices are explicitly given. Next, by employing the Kroneker product and successive low order basic matrices, the fast algorithms for the construction and decomposition of any high order circulant Pauli block Jacket matrices (CPBJMs) are systematically obtained. Finally, compared to the direct computation (DC), the proposed fast algorithms have a better efficiency, which may be available in many fields, such as signal sequence design, image compression, communication for coding and encoding, quantum signal processing and information theory.

Keywords: circulant block Jacket matrices; CBJMs; Pauli matrices; Jacket transform; Kronecker product; fast algorithms.

DOI: 10.1504/IJHPCN.2016.074657

International Journal of High Performance Computing and Networking, 2016 Vol.9 No.1/2, pp.45 - 51

Received: 15 Sep 2014
Accepted: 28 Oct 2014
Published online: 12 Feb 2016 *

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