An Optimized Algorithm to Construct QC-LDPC Matrix in Compressed Sensing
Aiming at the problems such as the large amount of data in transmission and difficulties in hardware implementation, an optimized algorithm is put forward to generate QC-LDPC measurement matrix based on limited geometry in compressed sensing, which can eliminate the short girth of 4 in Tanner graph through the design of basis matrix. Because of the quasi-cyclic characteristics, it can be realized by shift register so as to reduce the complexity of coding. The simulation results indicate that QC-LDPC matrix is superior to traditional measurement matrices by using the same OMP algorithm, and there are good improvements in the aspects of PSNR, SSIM, NMSE and runtime, which are conductive to the application of compressed sensing theory in real-time data transmission.
Dimakis A G, Smarandache R, Vontobel P O (2012). LDPC codes for compressed sensing. IEEE Transactions on Information Theory, 58(5), 3093-3114.
Li S, Gao F, Ge G, et al (2012). Deterministic Construction of Compressed Sensing Matrices via Algebraic Curves. IEEE Transactions on Information Theory, 58(8), 5035-5041.
Mo Q, Shen Y (2012). A Remark on the Restricted Isometry Property in Orthogonal Matching Pursuit. IEEE Transactions on Information Theory, 58(6), 3654–3656.
Monajemi H, Jafarpour S, Gavish M, et al (2013). Deterministic Matrices Matching the Compressed Sensing Phase Transitions of Gaussian Random Matrices. Proceedings of the National Academy of Sciences of the United States of America (PNAS), 110(4), 1181-1186.
Li S, Ge G (2014). Deterministic Sensing Matrices Arising From Near Orthogonal Systems. IEEE Transactions on Information Theory, 60(4), 2291-2302.
Amini A, Marvasti F (2011). Deterministic Construction of Binary, Bipolar, and Ternary Compressed Sensing Matrices. IEEE Transactions on Information Theory, 57(4), 2360-2370.
Xin-Ji Liu, Shu-Tao Xia, Fang-Wei Fu (2017). Reconstruction Guarantee Analysis of Basis Pursuit for Binary Measurement Matrices in Compressed Sensing. IEEE Transactions on Information Theory, 63 (5), 2922-2932.
Amini A, Montazerhodjat V, Marvasti F (2012). Matrices With Small Coherence Using p-Ary Block Codes. IEEE Transactions on Signal Processing, 60(1), 172–181.
Yu N Y, Zhao N (2013). Deterministic Construction of Real-Valued Ternary Sensing Matrices Using Optical Orthogonal Codes. IEEE Signal Processing Letters, 20(11), 1106-1109.
Mohades M M, Mohades A, Tadaion A (2014). A Reed-Solomon Code Based Measurement Matrix with Small Coherence. IEEE Signal Processing Letters, 21(7), 839-843.
Haiyang Liu, Hao Zhang, Lianrong Ma (2017). On the Spark of Binary LDPC Measurement Matrices From Complete Protographs. IEEE Signal Processing Letters, 24 (11), 1616-1620.
Rosnes E, Ambroze M A, Tomlinson M (2014). On the Minimum Stopping Distance of Array Low-Density Parity-Check Codes. IEEE Transactions on Information Theory, 60(9), 5204-5214.
Zhang Yi, Da Xinyu (2015). Construction of girth-eight QC-LDPC codes from arithmetic progression sequence with large column weight. Electronics Letters, 51(16), 1257-1259.
Tasdighi A, Banihashemi A H, Sadeghi M R (2017). Symmetrical constructions for regular girth-8 QC-LDPC codes. IEEE Transactions on Communications, 65(1), 14-22.
Needell D, Vershynin R (2010). Signal recovery from incomplete and inaccurate measurements via regularized orthogonal matching pursuit. IEEE Journal of Selected Topics in Signal Processing, 4(2), 310-316.