Application of compressed sensing on images via BCH measurement matrices

Khalid, Salman; Khan, Safiullah

doi:10.1109/icreate.2014.6828343

Cited by 4 publications

(4 citation statements)

References 8 publications

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“…where y(m 1 ) and y(m 2 ) are the multiplication results over GF(2 m 1 ) and GF(2 m 2 2 m 2 ), respectively. In (2), more precisely, an m 1 × m 1 binary matrix A i (m 1 ) is used for calculate the 1×m 1 binary matrix y(m 1 ) in GF(2 m 1 ). Note that A i (m 2 ) is also an m 1 × m 1 binary matrix even though it is targeting the constant multiplication over GF(2 m 2 ).…”

Section: The Proposed Sc and Cs Architectures For Multiple Gf Dimensionsmentioning

confidence: 99%

“…Note that G D (m 2 ) contains zero-extended multiplications over GF(2 m 2 ) as depicted in (2). To find the error positions, as shown in Fig.…”

Section: B the Proposed Parallel Dual-m Cs Architecturementioning

confidence: 99%

“…It is obvious that the similar way can be applied for the case of lower dimension. The only difference is that we have to consider the zero-extended multiplications as depicted in (2).…”

Section: B the Proposed Parallel Dual-m Cs Architecturementioning

confidence: 99%

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Area-Optimized Fully-Flexible BCH Decoder for Multiple GF Dimensions

Park

Lee

2018

IEEE Access

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Recently, there are increasing demands for fully flexible Bose-Chaudhuri-Hocquenghem (BCH) decoders, which can support different dimensions of Galois fields (GF) operations. As the previous BCH decoders are mainly targeting the fixed GF operations, the conventional techniques are no longer suitable for multiple GF dimensions. For the area-optimized flexible BCH decoders, in this paper, we present several optimization schemes for reducing hardware costs of multi-dimensional GF operations. In the proposed optimizations, we first reformulate the matrix operations in syndrome calculation and Chien search for sharing more common sub-expressions between GF operations having different dimensions. The cellbased multi-m GF multiplier is newly introduced for the area-efficient flexible key-equation solver. As case studies, we design several prototype flexible BCH decoders for digital video broadcasting systems and NAND flash memory controllers managing different page sizes. The implementation results show that the proposed fully-flexible BCH decoder architecture remarkably enhances the area-efficiency compared with the conventional solutions.INDEX TERMS Bose-Chaudhuri-Hocquenghem (BCH) decoder, Galois-field (GF) arithmetic, optimization, low complexity, VLSI design.

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Section: The Proposed Sc and Cs Architectures For Multiple Gf Dimensionsmentioning

confidence: 99%

“…Note that G D (m 2 ) contains zero-extended multiplications over GF(2 m 2 ) as depicted in (2). To find the error positions, as shown in Fig.…”

Section: B the Proposed Parallel Dual-m Cs Architecturementioning

confidence: 99%

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Area-Optimized Fully-Flexible BCH Decoder for Multiple GF Dimensions

Park

Lee

2018

IEEE Access

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“…CS has also strong ties to coding and information theory. The connections between coding and CS have been investigated in a limited number of papers such as [10], [66] [67]. One of the important concerns in CS theory is the existence of low-complexity algorithms for compressive sensing and reconstruction.…”

Section: Compressive Sensing and Coding Theorymentioning

confidence: 99%

Computationally Efficient and Secure Kronecker-based Compressive Sensing

Shahmirzadi¹

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We propose an efficient permuted Kronecker-based sparse measurement matrix for compressive sensing applications. We use sub-matrices to create a block-diagonal matrix and multiply it with a deterministic permutation matrix to measure the sparse or compressible signals. Using ECG signals from the MIT-BIH Arrhythmia database, we show that the reconstructed signal quality is comparable to the ones achieved using standard compressive sensing methods. Our methodology results in an overall reduction in storage and computations and can be generalized to other classes of eligible measurement matrices in compressive sensing. We show that with the use of a securely generated one-time sensing matrix, our proposed method is computationally secure against plaintext and ciphertext-only attacks. The proposed one-time sensing matrix is superior to other measurement matrices in the literature in terms of the number of linear feedback shift register bits required for their generation. vii 4.2 Histogram of 1,000,000 Gaussian random number samples using four B-bits LFSRs along with the auto correlation function. . . . . . . . . 4.3 Quality of recovered signal using S-OTS and our proposed method with Gaussian (A G ), Bernoulli (A Be ), and Bipolar (A Bi

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Circulant Euler-Jacket Transform and Its Applications Based on Fast Algorithm

Zhang

Liu

et al. 2015

Algorithms and Architectures for Parallel Processing

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Application of compressed sensing on images via BCH measurement matrices

Cited by 4 publications

References 8 publications

Area-Optimized Fully-Flexible BCH Decoder for Multiple GF Dimensions

Area-Optimized Fully-Flexible BCH Decoder for Multiple GF Dimensions

Computationally Efficient and Secure Kronecker-based Compressive Sensing

Circulant Euler-Jacket Transform and Its Applications Based on Fast Algorithm

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