• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.34 no.7C
• /
• pp.635-639
• /
• 2009

In this paper, we show that any two Hadamard matrices of the same size are equivalent if they have the property that the rows of each Hadamard matrix are closed under binary vector addition. One of direct consequences of this result is that the equivalence between cyclic Hadamard matrices constructed by maximal length sequences and Walsh-Hadamard matrix of the same size generated by Kronecker product can be established.

• Journal of the Korean Institute of Telematics and Electronics
• /
• v.26 no.10
• /
• pp.1617-1623
• /
• 1989

The introduction of the fast Fourier transform(FFT),an efficient computational algorithm for the discrete Fourier transform(DFT) by Cooley and Tukey(1965), has brought to the limelight various other discrete transforms. Some of the analog functions from which these transforms have been derived date back to the early 1920's, for example, Walsh functions (Walsh, 1923) and Hadamard Transform(Enomoto et al, 1965). Fast algorithms developed for the forward transform are equally applicable, exept for minor changes, to the inverse transform. In this paper, we present a simple pipelined Hadamard matrix(HM) which is used to develop a fast algorithm for the Hadamard Processor (HP). The Fast Hadamard Transform(FHT) can be derived using matrix partitioning techniques. The HP system is incorporated through a modular design which permits tailoring to meet a wide range of video data link applications. Emphasis has been placed on a low cost, a low power design suitable for airbone system and video codec.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.27 no.2A
• /
• pp.116-123
• /
• 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 Convergence Signal Processing
• /
• v.9 no.4
• /
• pp.304-312
• /
• 2008

Orthogonal codes like Walsh and Golay codes may have large correlation value when they are not synchronized, hence they are seldom used in asynchronous CDMA systems. Wysocki[1] showed that by multiplying the original Walsh-Hadamard matrix with an orthogonal transformation matrix the resultant matrix sustains orthogonality between row vectors and their cross-correlation can be reduced. Soberly and Wysocki[2] proposed similar scheme on Golay codes. This implies that using the proper orthogonal transformation cross-correlation of Walsh and Golay codes can be reduced, and the transformed codes can be used for user separation in the CDAM reverse link. In this paper we discuss cross-correlation related parameters which affect the performance of an asynchronous CDMA link, and we investigate the correlation properties of the transformed codes. When we designed orthogonal transformation matrices for Walsh and Golay codes, we minimized the maximum value of aperiodic cross-correlation of the codes ($ACC_{max}$) or the mean square value of the aperiodic cross-correlation($R_{cc}$) with preserving the orthogonality of the modified codes. We also evaluate the asynchronous CDMA system that uses the transformed Walsh and Golay codes.

• Journal of applied mathematics & informatics
• /
• v.7 no.1
• /
• pp.269-278
• /
• 2000

A Boolean function generates a binary sequence which is frequently used in a stream cipher. There are number of critical concepts which a Boolean function, as a key stream generator in a stream cipher, satisfies. These are nonlinearity, correlation immunity, balancedness, SAC(strictly avalanche criterion), PC(propagation criterion) and so on. In this paper, we present the algorithms for generating random nonlinear combining functions satisfying given correlation immune order and nonlinearity. These constructions can be applied for designing the key stream generators. We use Microsoft Visual C++6.0 for our program.

• Journal of the Institute of Electronics and Information Engineers
• /
• v.53 no.4
• /
• pp.106-114
• /
• 2016

In this paper, we propose an efficient integer inverse transform structure for vp9 decoder. The proposed structure is a hardware structure which is easy to control and requires less hardware resources, and shares algorithms for realizing entire DCT(Discrete Cosine Transform), ADST(Asymmetric Discrete Sine Transform) and WHT(Walsh-Hadamard Transform) in vp9. The integer inverse transform for vp9 google model has a fast structure, named butterfly structure. The integer inverse transform for google C model, unlike universal fast structure, takes a constant rounding shift operator on each stage and includes an asymmetrical sine transform structure. Thus, the proposed structure approximates matrix coefficient values for all transform mode and is used to matrix operation method. With the proposed structure, shared operations for all inverse transform algorithm modes can be possible with reduced number of multipliers compared to the butterfly structure, which in turn manages the hardware resources more efficiently.

• The KIPS Transactions:PartB
• /
• v.8B no.3
• /
• pp.305-310
• /
• 2001

본 논문에서는 직접행렬 대역확산 방식을 사용하여 Hadamard-Walsh 행렬을 워터마크 영상에 첨가한 후, 주파수 영역에서 원 영상에 삽입하고 복원하는 새로운 이미지 워터마킹 기법을 제안한다. 워터마크 영상은 시각적으로 인식 가능한 패턴(마크, 로고, 심볼, 인장 또는 서명)을 사용한다. 워터마크가 삽입된 영상의 화질저하를 추정하기 위해 PSNR(Peak Signal to Noise Ratio)을 계산하고, 복원된 워터마크의 복원률(reconstructive rate)을 구하여 외부공격에 대한 워터마크의 강인성을 확인한다. 표준영상에 적용해 본 결과, 워터마크가 삽입된 영상의 PSNR은 93.2dB로 우수한 화질을 얻을 수 있었으며 JPEG 손실 압축에서는 78.1% 이상의 워터마크 복원률을 얻을 수 있었고 영상변형 및 임펄스 잡음하에서도 효과적인 워터마크 복원 능력을 보였다.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.15 no.3
• /
• pp.221-231
• /
• 1990

In this paper, A new 2-D DCT algorithm is proposed to reduce the computational amount of transform operation using the distribution of the motion compensated error signal and the bit allocation table. In the this algorithm, 2-D Walsh-Hadamard transform is directly computed and then multiplied by a constant matrix. Multiplications are concentrated on the final stage in thie algorithm, thus the computational amount is reduced in proportion to the number of transform coefficients that are excluded from quatization. The computational amount in computing only the DCT coefficients allocated to the bit allocation table is calculated. As the result, the number of multiplications is less thn the algorithm known to have the fewest number of computations when less than 0.6 bits per pixel are allocated to tranform coding for the motion compensated error image in the case of the proposed algorithm. Thus, it shows that the proposed algorithm is valid in reducing the computational loads of transform coding.

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