• Journal of electromagnetic engineering and science
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• v.6 no.4
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• pp.244-252
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• 2006

A block Jacket transform and. its block inverse Jacket transformn have recently been reported in the paper 'Fast block inverse Jacket transform'. But the multiplication of the block Jacket transform and the corresponding block inverse Jacket transform is not equal to the identity transform, which does not conform to the mathematical rule. In this paper, new binary block Jacket transforms and the corresponding binary block inverse Jacket transforms of orders $N=2^k,\;3^k\;and\;5^k$ for integer values k are proposed and the mathematical proofs are also presented. With the aid of the Kronecker product of the lower order Jacket matrix and the identity matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse, fast algorithm and prime based $P^k$ order of proposed binary block inverse Jacket transform, it can be applied in communications such as space time block code design, signal processing, LDPC coding and information theory. Application of circular permutation matrix(CPM) binary low density quasi block Jacket matrix is also introduced in this paper which is useful in coding theory.

• Proceedings of the IEEK Conference
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• 2001.09a
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• pp.769-772
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• 2001

Waish-Hadamard Transform은 압축, 필터링, 코드 디자인 등 다양한 이미지처리 분야에 응용되어왔다. 이러한 Hadamard Transform을 기본으로 확장한 Jacket Transform은 행렬의 원소에 가중치를 부여함으로써 Weighted Hadamard Matrix라고 한다. Jacket Matrix의 cocyclic한 특성은 암호화, 정보이론, TCM 등 더욱 다양한 응용분야를 가질 수 있고, Space Time Code에서 대역효율, 전력면에서도 효율적인 특성을 나타낸다 [6],[7]. 본 논문에서는 Distributed Arithmetic(DA) 구조를 이용하여 Fast Jacket Transform(FJT)을 구현한다. Distributed Arithmetic은 ROM과 어큐뮬레이터를 이용하고, Jacket Watrix의 행렬을 분할하고 간략화하여 구현함으로써 하드웨어의 복잡도를 줄이고 기존의 시스톨릭한 구조보다 면적의 이득을 얻을 수 있다. 이 방법은 수학적으로 간단할 뿐 만 아니라 행렬의 곱의 형태를 단지 덧셈과 뺄셈의 형태로 나타냄으로써 하드웨어로 쉽게 구현할 수 있다. 이 구조는 입력데이타의 워드길이가 n일 때, O(2n)의 계산 복잡도를 가지므로 기존의 시스톨릭한 구조와 비교하여 더 적은 면적을 필요로 하고 FPGA로의 구현에도 적절하다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.7A
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• pp.1250-1256
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• 2001

개선된 리버스 자켓 행렬(Reverse Jacket matrix)의 정의와 함께 그의 역행렬을 소개한다. 새로이 정의된 리버스 자켓 행렬은 실베스터 타입의 하다마드 행렬을 이용하여 더욱 일반화되었다. 이 논문에서는 고속 리버스 자켓 변환(fast Reverse Jacket transform)을 제시하며 또한 이 알고리즘이 4점 이산 푸리에 변환으로 응용이 됨을 보여준다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.4B
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• pp.423-426
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• 2001

본 논문에서는 고속 리버스 자켓 역변환(inverse fast Reverse Jacket transform, 간략히 IFRJT)을 제안하며 이방법은 역변환을 explicit 하게 표현한다. 이 알고리즘의 장점은 중앙가중치 하다마드 변환보다 더 빠르고 쉽게 주어진 행렬의 역을 구한다는 점이다. 우리는 얼마나 간단히 IFRJT를 얻을 수 있는지를 예제를 통해 보여준다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.26 no.4B
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• pp.418-422
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• 2001

4-점 리버스 자켓 변환 (4-Point Reverse Jacket transform)의 장점 중의 하나는 4-점 fast Fourier transform(FFT)시 야기되는 실수 또는 복소수 곱셈을 행렬분해(matrix decomposition)를 이용, 곱셈인자를 모두 대각행렬에만 집중시킨, 매우 간결하고 효율적인 알고리즘이라는 점이다. 본 논문에서는 이를 N 점 FFT에 적용하는 알고리즘을 제안한다. 이 방법은 기존의 다른 변환형태보다 확장하거나 구조를 파악하기에 매우 용이하다.

• 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.

• Journal of Communications and Networks
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• v.13 no.5
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• pp.449-455
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• 2011

Inspired by fast Jacket transforms, we propose simple factorization and construction algorithms for the M-dimensional discrete Fourier transform (DFT) matrices underlying generalized Chinese remainder theorem (CRT) index mappings. Based on successive coprime-order DFT matrices with respect to the CRT with recursive relations, the proposed algorithms are presented with simplicity and clarity on the basis of the yielded sparse matrices. The results indicate that our algorithms compare favorably with the direct-computation approach.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.2A
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• pp.116-123
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• 2002

The jacket matrix is based on the Walsh-Hadamard matrix and an extension of it. While elements of the Walsh-Hadamard matrix are +1, or -1, those of the Jacket matrix are ${\pm}$1 and ${\pm}$$\omega$, which is $\omega$, which is ${\pm}$j and ${\pm}$2$\sub$n/. This matrix has weights in the center part of the matrix and its size is 1/4 of Hadamard matrix, and it has also two parts, sigh and weight. In this paper, instead of the conventional Jacket matrix where the weight is imposed by force, a simple Jacket sequence generation method is proposed. The Jacket sequence is generated by AND and Exclusive-OR operations between the binary indices bits of row and those of column. The weight is imposed on the element by when the product of each Exclusive-OR operations of significant upper two binary index bits of a row and column is 1. Each part of the Jacket matrix can be represented by jacket sequence using row and column binary index bits. Using Distributed Arithmetic (DA), we present a VLSI architecture of the Fast Jacket transform is presented. The Jacket matrix is able to be applied to cryptography, the information theory and complex spreading jacket QPSK modulation for WCDMA.

• Journal of electromagnetic engineering and science
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• v.5 no.4
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• pp.166-171
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• 2005

In this paper, a set of new complementary quadriphase sequences based on Jacket matrix is proposed. It is with a good zero cross correlation zone and efficiently eliminates the inter-user interferences for CDMA systems. Unlike the conventional complementary sequence designs, the proposed sequences can be easily extended to large odd and even sizes by using a fast linear transform for multi-user communication systems. The computer simulation shows that the proposed sequences have better performance than conventional multi-user spreading CDMA systems using ZCZ sequence.

• 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.