• Journal of electromagnetic engineering and science
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• v.7 no.1
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• pp.17-27
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• 2007

Jacket matrices which are defined to be $n{\times}n$ matrices $A=(a_{jk})$ over a field F with the property $AA^+=nI_n$ where $A^+$ is the transpose matrix of elements inverse of A,i.e., $A^+=(a_{kj}^-)$, was introduced by Lee in 1984 and are used for signal processing and coding theory, which generalized the Hadamard matrices and Center Weighted Hadamard matrices. In this paper, some properties and constructions of Jacket matrices are extensively investigated and small orders of Jacket matrices are characterized, also present the full rate and the 1/2 code rate complex orthogonal space time code with full diversity.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.15 no.4
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• pp.119-125
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• 2015

In this paper, we introduce a Hadamard matrix interstream transmission based blind channel estimation for multi-cells multiple-input and multiple-output (MIMO) networks. The proposed scheme is based on a network with mobile stations (MS) which are deployed with multi cells. We assume that the MS have the signals from both cells. The signal from near cell are considered as desired signal and the signals from the other cells are interference signal. Since the channel is blind, so that we transmit Hadamard matrix pattern pilot stream to estimate the channel; that gives easier and fast channel estimation for large scale MIMO channel. The computation of Hadamard based system takes only complex additions, and thus the complexity of which is much lower than the scheme with Fourier transform since complex multiplications are not needed. The numerical analysis will give perfection of proposed channel estimation.

• Journal of Communications and Networks
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• v.12 no.3
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• pp.240-245
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• 2010

Jacket matrices, motivated by the complex Hadamard matrix, have played important roles in signal processing, communications, image compression, cryptography, etc. In this paper, we suggest a novel approach to design a simple class of space-time block codes (STBCs) to reduce its peak-to-average power ratio. The proposed code provides coding gain due to the characteristics of the complex Hadamard matrix, which is a special case of Jacket matrices. Also, it can achieve full rate and full diversity with the simple decoding. Simulations show the good performance of the proposed codes in terms of symbol error rate. For generality, a kind of quasi-orthogonal STBC may be similarly designed with the improved performance.

• 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 the Institute of Electronics and Information Engineers
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• v.50 no.7
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• pp.19-26
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• 2013

In this paper we prove that all Jacket matrices are circulant and up to equivalence. This result leads to new constructions of Toeplitz Jacket(TJ) matrices. We present the construction schemes of Toeplitz Jacket matrices and the examples of $4{\times}4$ and $8{\times}8$ Toeplitz Jacket matrices. As a corollary we show that a Toeplitz real Hadamard matrix is either circulant or negacyclic.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.11 no.5
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• pp.2468-2483
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• 2017

The construction of completely random sensing matrices of Compressive Sensing requires a large number of random numbers while that of deterministic sensing operators often needs complex mathematical operations. Thus both of them have difficulty in acquiring large signals efficiently. This paper focuses on the enhancement of the practicability of the structurally random matrices and proposes a semi-deterministic sensing matrix called Partial Kronecker product of Identity and Hadamard (PKIH) matrix. The proposed matrix can be viewed as a sub matrix of a well-structured, sparse, and orthogonal matrix. Only the row index is selected at random and the positions of the entries of each row are determined by a deterministic sequence. Therefore, the PKIH significantly decreases the requirement of random numbers, which has a complex generating algorithm, in matrix construction and further reduces the complexity of sampling. Besides, in order to process large signals, the corresponding fast sampling algorithm is developed, which can be easily parallelized and realized in hardware. Simulation results illustrate that the proposed sensing matrix maintains almost the same performance but with at least 50% less random numbers comparing with the popular sampling matrices. Meanwhile, it saved roughly 15%-35% processing time in comparison to that of the SRM matrices.

• The Journal of the Korea institute of electronic communication sciences
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• v.7 no.2
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• pp.317-325
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• 2012

In this paper, we consider the encoding scheme of Low Density Parity Check codes. In particular, using the Jacket Pattern and circulant permutation matrices, we propose the simple encoding scheme of Richardson's lower triangular matrix. These encoding scheme can be extended to a flexible code rate. Based on the simple matrix process, also we can design low complex and simple encoders for the flexible code rates.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.1C
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• pp.1-8
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• 2003

In this paper, performance of the CPC(complex phase code) which is recently proposed as a practical phase encoding method for phase-code multiplexes holographic memory system is comparatively analyzed with those of the conventional phase codes such as PR(pure random code), RCE(random code with equality), WHM(Walsh Hadamard Matrix). In computer simulation, the size of an address bean is fixed at 32$\times$32 pixels and 0%-25% phase-error ratio in a pixel are intentionally added to the real phase values to consider the nonlinear phase-modulation characteristics of the practical spatial light modulator. From comparative analysis of crosstalks and signal-to-noise ratios for these phase codes by calculating auto-correlation and cross-correlation, it is found that the CPC have the lowest cross-correlation mean value of 0.021, the lowest standard deviation of 0.0113 and the highest signal-to-noise ratio(SNR) of 27.4 among the four types of phase code. In addition, from the calculation of the number of all possible address beams for these four types of phase code as the size of the address beam is fixed to 3232 pixels, the CPC is found to have 6.334$\times$10$^{49}$ address beams, which are relatively higher number than that of the conventional phase codes.