NDLI: Deterministic construction of array QC CS measurement matrices based on Singer perfect difference sets

Content Provider	IET Digital Library
Author	Torshizi, Ehsan Olyaei Tinati, Mohammad Ali Meshgini, Saeed
Abstract	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.
Starting Page	2512
Ending Page	2522
Page Count	11
ISSN	17518628
Volume Number	13
e-ISSN	17518636
Issue Number	Issue 16, Oct (2019)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/iet-com/13/16
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/iet-com.2018.6015
Journal	IET Communications
Publisher Date	2019-06-26
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	Algebra Array QC CS Measurement Matrices Array Quasicyclic LDPC Codes Circulant Permutation Matrices Code Common Environments Compressed Sensing Computationally Tractable Criteria CS Recovery Capabilities Cyclic Codes Deterministic Construction Deterministic Matrices Deterministic Sparse Sensing Matrices Low-density Parity-check Code Measurement Matrix Parity Check Code Physical Storage Space Restricted Isometric Property Sensing Matrix Signal Processing And Detection Singer Perfect Difference Sets Sparse Matrix Superior CS Recovery Ability
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering Computer Science Applications

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