• Communications for Statistical Applications and Methods
• /
• v.23 no.2
• /
• pp.105-117
• /
• 2016

In the paper, as a sequence of the first tutorial, we discuss sufficient dimension reduction methodologies used to estimate central subspace (sliced inverse regression, sliced average variance estimation), central mean subspace (ordinary least square, principal Hessian direction, iterative Hessian transformation), and central $k^{th}$-moment subspace (covariance method). Large-sample tests to determine the structural dimensions of the three target subspaces are well derived in most of the methodologies; however, a permutation test (which does not require large-sample distributions) is introduced. The test can be applied to the methodologies discussed in the paper. Theoretical relationships among the sufficient dimension reduction methodologies are also investigated and real data analysis is presented for illustration purposes. A seeded dimension reduction approach is then introduced for the methodologies to apply to large p small n regressions.

• Bulletin of the Korean Mathematical Society
• /
• v.26 no.1
• /
• pp.35-42
• /
• 1989

Let .ohm.$_{n}$ and Pm $t_{n}$ denote the sets of all n*n doubly stochastic matrices and the set of all n*n permutation matrices respectively. For m*n matrices A=[ $a_{ij}$ ], B=[ $b_{ij}$ ] we write A.leq.B(A$a_{ij}$ .leq. $b_{ij}$ ( $a_{ij}$ < $b_{ij}$ ) for all i=1,..,m; j=1,..,n. Let $I_{n}$ denote the identity matrix of order n, let $J_{n}$ denote the n*n matrix all of whose entries are 1/n, and let $K_{n}$=n $J_{n}$. For a complex square matrix A, the permanent of A is denoted by per A. Let $E_{ij}$ denote the matrix of suitable size all of whose entries are zeros except for the (i,j)-entry which is one.hich is one.

• Journal of the Korean Mathematical Society
• /
• v.56 no.2
• /
• pp.507-521
• /
• 2019

For any $m{\times}n$ nonbinary Boolean matrix A, its spanning column rank is the minimum number of the columns of A that spans its column space. We have a characterization of spanning column rank-1 nonbinary Boolean matrices. We investigate the linear operators that preserve the spanning column ranks of matrices over the nonbinary Boolean algebra. That is, for a linear operator T on $m{\times}n$ nonbinary Boolean matrices, it preserves all spanning column ranks if and only if there exist an invertible nonbinary Boolean matrix P of order m and a permutation matrix Q of order n such that T(A) = PAQ for all $m{\times}n$ nonbinary Boolean matrix A. We also obtain other characterizations of the (spanning) column rank preserver.

• Journal of electromagnetic engineering and science
• /
• v.7 no.1
• /
• pp.28-34
• /
• 2007

In this paper, we present a quasi-Jacket block matrices over binary matrices which all are belong to a class of cocyclic matrices is the same as the Hadamard case and are useful in digital signal processing, CDMA, and coded modulation. Based on circular permutation matrix(CPM) cocyclic quasi block low-density matrix is introduced in this paper which is useful in coding theory. Additionally, we show that the fast algorithm of quasi-Jacket block matrix.

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

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

• Journal of Communications and Networks
• /
• v.17 no.6
• /
• pp.634-646
• /
• 2015

Assuming perfect channel state information (CSI) at the transmitter and receiver, the optimization problem of maximizing the minimum Euclidean distance between two received signals by a linear precoder is considered for multiple-input multiple-output (MIMO) systems with arbitrary dimensions and arbitraryary quadrature amplitude modulation (QAM) input. A general precoding framework is first presented based on the Gram matrix, which is shown for 2-dimensional (2-D) and 3-dimensional (3-D) MIMO systems when employing the ellipse expanding method (EEM). An extended precoder for high-dimensional MIMO system is proposed following the precoding framework, where the Gram matrix for high-dimensional precoding matrix can be generated through those chosen from 2-D and 3-D results in association with a permutation matrix. A complexity-reduced maximum likelihood detector is also obtained according to the special structure of the proposed precoder. The analytical and numerical results indicate that the proposed precoder outperforms the other precoding schemes in terms of both minimum distance and bit error rate (BER).

• Journal of the Korea Institute of Information Security & Cryptology
• /
• v.15 no.1
• /
• pp.99-107
• /
• 2005

ARIA is a 128-bit block cipher having 128-bit, 192-bit, or 256-bit key length. The cipher is a substitution and permutation encryption network (SPN) and uses an involutional binary matrix. This structure was efficiently developed into light weight environments or hardware implementations. This paper shows that a careless implementation of an ARIA on smartcards is vulnerable to a differential power analysis attack This attack is realistic because we can measure power consumption signals at two kinds of S-boxes and two types of substitution layers. By using the two round key, we extracted the master key (MK).

• Journal of Information Processing Systems
• /
• v.18 no.1
• /
• pp.59-74
• /
• 2022

During the last decade, the security of digital images has received considerable attention in various multimedia transmission schemes. However, many current cryptosystems tend to adopt a single-layer permutation or diffusion algorithm, resulting in inadequate security. A hierarchical bilateral diffusion architecture for color image encryption is proposed in response to this issue, based on a hyperchaotic system and DNA sequence operation. Primarily, two hyperchaotic systems are adopted and combined with cipher matrixes generation algorithm to overcome exhaustive attacks. Further, the proposed architecture involves designing pixelpermutation, pixel-diffusion, and DNA (deoxyribonucleic acid) based block-diffusion algorithm, considering system security and transmission efficiency. The pixel-permutation aims to reduce the correlation of adjacent pixels and provide excellent initial conditions for subsequent diffusion procedures, while the diffusion architecture confuses the image matrix in a bilateral direction with ultra-low power consumption. The proposed system achieves preferable number of pixel change rate (NPCR) and unified average changing intensity (UACI) of 99.61% and 33.46%, and a lower encryption time of 3.30 seconds, which performs better than some current image encryption algorithms. The simulated results and security analysis demonstrate that the proposed mechanism can resist various potential attacks with comparatively low computational time consumption.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.31 no.1C
• /
• pp.14-19
• /
• 2006

The high encoding complexity of LDPC codes can be solved by designing structured parity-check matrix. If the parity-check matrix of LDPC codes is composed of same type of blocks, decoder implementation can be simple, this structure allow structured decoding and required memory for storing the parity-check matrix can be reduced largely. In this parer, we propose a construction algorithm for short block length structured LDPC codes based on girth condition, PEG algorithm and variable node connectivity. The code designed by this algorithm shows similar performance to other codes without structured constraint in low SNR and better performance in high SNR than those by simulation