%0 Electronic Article
%A Ehsan Olyaei Torshizi
%A Mohammad Ali Tinati
%A Saeed Meshgini
%K circulant permutation matrices
%K compressed sensing
%K Singer perfect difference sets
%K CS recovery capabilities
%K measurement matrix
%K array quasicyclic LDPC codes
%K superior CS recovery abilities
%K deterministic construction
%K common environments
%K low-density parity-check codes
%K deterministic matrices
%K deterministic sparse sensing matrices
%K sensing matrix
%K restricted isometric property
%K computationally tractable criteria
%K physical storage space
%K array QC CS measurement matrices
%X Low-density parity-check (LDPC) codes and compressed sensing (CS) share many common environments. In this study, a novel approach for constructing a new class of deterministic sparse sensing matrices based on array quasi-cyclic (QC) LDPC codes via Singer perfect difference sets is proposed. In contrast to random and the other deterministic matrices, the proposed framework would be highly desirable as it is generated based on circulant permutation matrices, which requires less memory for storage and lower computational cost for sensing. Since the restricted isometric property is very difficult to verify, then the mutual coherence and the girth are two computationally tractable criteria that the authors used to assess the CS recovery capabilities of sensing matrices. In addition, inspired by LDPC codes, they extract a necessary condition for the proposed measurement matrix to have effective values for girth as large as g ≥ 6 and 8 . Comprehensive one-dimensional (1D) and 2D simulations verify that their proposed sensing matrix has minimum coherence and superior CS recovery abilities in comparison with the corresponding random Gaussian, Bernoulli, and the other deterministically generated matrices. Furthermore, the required physical storage space and the complexity of the hardware implementation are greatly reduced due to being sparse and QC in structure.
%@ 1751-8628
%T Deterministic construction of array QC CS measurement matrices based on Singer perfect difference sets
%B IET Communications
%D June 2019
%I Institution of Engineering and Technology
%U https://digital-library.theiet.org/;jsessionid=29rcsf1t580tm.x-iet-live-01content/journals/10.1049/iet-com.2018.6015
%G EN