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Measurement Matrices Construction for Compressed Sensing Based on Finite Field QuasiCyclic LDPC Codes
Hua XU Hao YANG Wenjuan SHI
Publication
IEICE TRANSACTIONS on Communications
Vol.E99B
No.11
pp.23322339 Publication Date: 2016/11/01
Online ISSN: 17451345 Type of Manuscript: PAPER Category: Fundamental Theories for Communications Keyword: compressed sensing, mutual coherence, finite field QCLDPC codes, compression ratio,
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Summary:
Measurement matrix construction is critically important to signal sampling and reconstruction for compressed sensing. From a practical point of view, deterministic construction of the measurement matrix is better than random construction. In this paper, we propose a novel deterministic method to construct a measurement matrix for compressed sensing, CSFF (compressed sensingfinite field) algorithm. For this proposed algorithm, the constructed measurement matrix is from the finite field Quasicyclic Low Density Parity Check (QCLDPC) code and thus it has quasicyclic structure. Furthermore, we construct three groups of measurement matrices. The first group matrices are the proposed matrix and other matrices including deterministic construction matrices and random construction matrices. The other two group matrices are both constructed by our method. We compare the recovery performance of these matrices. Simulation results demonstrate that the recovery performance of our matrix is superior to that of the other matrices. In addition, simulation results show that the compression ratio is an important parameter to analyse and predict the recovery performance of the proposed measurement matrix. Moreover, these matrices have less storage requirement than that of a random one, and they achieve a better tradeoff between complexity and performance. Therefore, from practical perspective, the proposed scheme is hardware friendly and easily implemented, and it is suitable to compressed sensing for its quasicyclic structure and good recovery performance.

