• Proceedings of the KIEE Conference
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• 2007.04a
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• pp.281-282
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• 2007

We address a new representation of DCT/DFT/Wavelet matrices via one hybrid architecture. Based on an element inverse matrix factorization algorithm, we show that the OCT, OFT and Wavelet which based on Haar matrix have the similarrecursive computational pattern, all of them can be decomposed to one orthogonal character matrix and a special sparse matrix. The special sparse matrix belongs to Jacket matrix, whose inverse can be from element-wise inverse or block-wise inverse. Based on this trait, we can develop a hybrid architecture.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.3
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• pp.203-211
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• 2016

The genetic code is a key to bio-informatics and to a science of biological self-organizing on the whole. Modern science faces the necessity of understanding and systematically explaining mysterious features of ensembles of molecular structures of the genetic code. This paper is devoted to symmetrical analysis for genetic systems. Mathematical theories of noise-immunity coding and discrete signal processing are based on Jacket matrix methods of representation and analysis of information. Both of the RNA and Jacket Matrix property also have the Element(Block) - wise Inverse Matrices. These matrix methods, which are connected closely with relations of symmetry, are borrowed for a matrix analysis of ensembles of molecular elements of the genetic code. This method is presented for its simplicity and the clarity with which it decomposes a Jacket Matrix in terms of the genetic RNA Codon.

• Journal of Broadcast Engineering
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• v.16 no.5
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• pp.782-792
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• 2011

In this paper, we address a new fast DCT-II/DFT/HWT hybrid transform architecture for digital video and fusion mobile handsets based on Jacket-like sparse matrix decomposition. This fast hybrid architecture is consist of source coding standard as MPEG-4, JPEG 2000 and digital filtering discrete Fourier transform, and has two operations: one is block-wise inverse Jacket matrix (BIJM) for DCT-II, and the other is element-wise inverse Jacket matrix (EIJM) for DFT/HWT. They have similar recursive computational fashion, which mean all of them can be decomposed to Kronecker products of an identity Hadamard matrix and a successively lower order sparse matrix. Based on this trait, we can develop a single chip of fast hybrid algorithm architecture for intelligent mobile handsets.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.3
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• pp.25-33
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• 2015

As a reversible Jacket is having the compatibility of two sided wearing, the matrix that both the inside and the outside are compatible is called Jacket matrix, and the matrix is having both inside and outside by the processes of element-wise inverse and block-wise inverse. This concept had been completed by one of the authors Moon Ho Lee in 1989, and finally that resultant matrix has been christened as Jacket matrix, in 2000. This is the most generalized extension of the well known Hadamard matrices, which includes both orthogonal and non-orthogonal matrices. This matrix addresses many problems in information and communication theories. we investigate the properties of the Jacket matrix, i.e. determinants, eigenvalues, and kronecker product. These computations are very useful for signal processing and orthogonal codes design. In our proposal, we provide some results to calculate these values by using a very simple mathematical model with less complexity.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.49 no.3
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• pp.14-26
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• 2012

In this paper, a fast diagonal-weighted Jacket matrices (DWJMs) is proposed to have the orthogonal architecture. We develop the successive DWJM to reduce the computational load while factorizing the large-order DWJMs into the low-order sparse matrices with the fast algorithms. The proposed DWJM is then applied to the precoding multiple-input and multiple output (MIMO) wireless communications because of its diagonal-weighted framework with element-wise inverse characteristics. Based on the properties of the DWJM, the DWJM can be used as alternative open loop cyclic delay diversity (CDD) precoding, which has recently become part of the cellular communications systems. Performance of the DWJM-based precoding system is verified for orthogonal space-time block code (OSTBC) MIMO LTE systems.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.6
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• pp.69-78
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• 2017

Shannon of the 5G smartphone and Fourier of the signal processing meet in the sampling theorem (2 times the highest frequency 1). In this paper, the initial Shannon Theorem finds the Shannon capacity at the point-to-point, but the 5G shows on the Relay channel that the technology has evolved into Multi Point MIMO. Fourier transforms are signal processing with fixed parameters. We analyzed the performance by proposing a 2N-1 multivariate Fourier-Jacket transform in the multimedia age. In this study, the authors tackle this signal processing complexity issue by proposing a Jacket-based fast method for reducing the precoding/decoding complexity in terms of time computation. Jacket transforms have shown to find applications in signal processing and coding theory. Jacket transforms are defined to be $n{\times}n$ matrices $A=(a_{jk})$ over a field F with the property $AA^{\dot{+}}=nl_n$, where $A^{\dot{+}}$ is the transpose matrix of the element-wise inverse of A, that is, $A^{\dot{+}}=(a^{-1}_{kj})$, which generalise Hadamard transforms and centre weighted Hadamard transforms. In particular, exploiting the Jacket transform properties, the authors propose a new eigenvalue decomposition (EVD) method with application in precoding and decoding of distributive multi-input multi-output channels in relay-based DF cooperative wireless networks in which the transmission is based on using single-symbol decodable space-time block codes. The authors show that the proposed Jacket-based method of EVD has significant reduction in its computational time as compared to the conventional-based EVD method. Performance in terms of computational time reduction is evaluated quantitatively through mathematical analysis and numerical results.