• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.6
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• pp.319-327
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• 2016

In this paper we investigate that most of plants and animals have the symmetric property, such as a tree or a sheep's horn. In addition, the human body is also symmetric and contains the DNA. We can see the logarithm helices in Fibonacci series and animals, and helices of plants. The sunflower has a shape of circle. A circle is circular symmetric because the shapes are same when it is shifted on the center. Einstein's spatial relativity is the relation of time and space conversion by the symmetrically generalization of time and space conversion over the spacial. The left and right helices of plants and animals are the symmetric and have element-wise inverse relationships each other. The weight of center weight Hadamard matrix is 2 and is same as the base 2 of natural logarithm. The helix matrices are symmetric and have element-wise inverses.

• 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.

• 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.

• 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.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.1
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• pp.15-20
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• 2016

Compared to the MIMO system using the spatial multiplexing methods and the MIMO system using the diversity scheme achieved a high rate, but the lower the diversity gain to improve the data transmission reliability should separate the spatial stream at the MIMO receiver. In this paper, we compared Channel capacity detection methods with the Lattice code, the 3-user interference channel and linear channel interference detection methods ZF (Zero Forcing) and MMSE (Minimum Mean Square Error) detection methods. The channel is a Diagonal channel. In other words, Diagonal channel is confirmed by the inverse matrix satisfies the properties of Jacket are element-wise inverse to $[H]_N[H]_N^{-1}=[I]_N$.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.21 no.2
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• pp.103-109
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• 2021

About the orthogonal Hadamard matrix announced by Hadamard in France in 1893, Professor Moon Ho Lee newly defined it as Center Weight Hadamard in 1989 and announced it, and discovered the Jacket matrix in 1998. The Jacket matrix is a generalization of the Hadamard matrix. In this paper, we propose a method of obtaining the Symmetric Jacket matrix, analyzing important properties and patterns, and obtaining the Jacket matrix's determinant and Eigenvalue, and proved it using Eigen decomposition. These calculations are useful for signal processing and orthogonal code design. To analyze the matrix system, compare it with DFT, DCT, Hadamard, and Jacket matrix. In the symmetric matrix of Galois Field, the element-wise inverse relationship of the Jacket matrix was mathematically proved and the orthogonal property AB=I relationship was derived.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.5
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• pp.39-49
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• 2015

Some characters and construction theorems of Pseudo Jacket Matrix which is generalized from Jacket Matrix introduced by Jacket Matrices: Construction and Its Application for Fast Cooperative Wireless signal Processing[27] was announced. In this paper, we proposed some examples of Pseudo inverse Jacket matrix, such as $2{\times}4$, $3{\times}6$ non-square matrix for the MIMO channel. Furthermore we derived MIMO singular value decomposition (SVD) pseudo inverse channel and developed application to utilize SVD based on channel estimation of partitioned antenna arrays. This can be also used in MIMO channel and eigen value decomposition (EVD).

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.1
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• pp.59-68
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• 2017

The flower and woman are beautiful but Euler's theorem and the symmetry are the best. Shannon applied his theorem to information and communication based on Euler's theorem. His theorem is the root of wireless communication and information theory and the principle of today smart phone. Their meeting point is $e^{-SNR}$ of MIMO(multiple input and multiple output) multiple antenna diversity. In this paper, Euler, who discovered the most beautiful formula($e^{{\pi}i}+1=0$) in the world, briefly guided Shannon's formula ($C=Blog_2(1+{\frac{S}{N}})$) to discover the origin of wireless communication and information communication, and these two masters prove a meeting at the Shannon limit, It reveals something what this secret. And we find that it is symmetry and element-wise inverse are the hidden secret in algebraic coding theory and triangular function.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.47 no.7
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• pp.93-101
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• 2010

In this paper we generate Gold-sequence by using M-sequence which is made by two primitive polynomial of GF(2). Generally M-sequence is generated by linear feedback shift register code generator. Here we show that this matrix of appropriate permutation has Hadamard matrix property. This matrix proves that Gold-sequence through two M-sequence and additive matrix of one column has one of major properties of Hadamard matrix, orthogonal. and this matrix show another property that multiplication with one matrix and transpose matrix of this matrix have the result of unit matrix. Also M-sequence which is made by linear feedback shift register gets Hadamard matrix property mentioned above by adding matrices of one column and one row. And high-speed conversion is possible through L-matrix and the S-matrix.