Walsh Hadamard Transform Based Transceiver Design for SC-FDMA with Discrete Wavelet Transform

This article proposes a new transceiver design for Single carrier frequency division multiple access(SCFDMA)system based on discrete wavelet transform(DWT). SCFDMA offers almost same structure as Orthogonal frequency division multiple access(OFDMA)with extra advantage of low Peak to Average Power Ratio(PAPR). Moreover,this article also suggests the application of Walsh Hadamard transform(WHT)for linear precoding(LP)to improve the PAPR performance of the system. Supremacy of the proposed transceiver over conventional Fast Fourier transform(FFT)based SCFDMA is shown through simulated results in terms of PAPR,spectral efficiency(SE)and bit error rate(BER).

On the Value Distributions of Walsh Spectrum of Two Classes of Plateaued Functions

Based on the properties of trace functions and quadratic forms, this paper presents value distributions of Walsh spectrum of the Plateaued functions of the form Tr（R（x）） with n=3r or 4r variables, where r 〉 1 is an odd integer. Our results can be used to determine the numbers of non-zero Walsh spectrum values and the nonlinearities of these functions, and estimate their resiliency orders. Especially, the value distributions can be used to deduce the tight lower bounds of the second order nonlinearity of two classes of Boolean functions. It is demonstrated that our bounds are better than the previously obtained bounds.

A Characterization of MRA Based Wavelet Frames Generated by the Walsh Polynomials

Extension Principles play a significant role in the construction of MRA based wavelet frames and have attracted much attention for their potential applications in various scientific fields. A novel and simple procedure for the construction of tight wavelet frames generated by the Walsh polynomials using Extension Principles was recently considered by Shah in [Tight wavelet frames generated by the Walsh poly- nomials, Int. J. Wavelets, Multiresolut. Inf. Process., 11（6） （2013）, 1350042]. In this paper, we establish a complete characterization of tight wavelet frames generated by the Walsh polynomials in terms of the polyphase matrices formed by the polyphase components of the Walsh polynomials.

A Proof for the Nonexistence of Some Homogeneous Bent Functions

By the relationship between the first linear spectra of a function at partialpoints and the Hamming weights of the sub-functions, and by the Hamming weight of homogenousBoolean function, it is proved that there exist no homogeneous bent functions ofdegree in in n = 2mvariables for m >3.

PGOPO Approach to Design Linear Servomechanism of Time-Varying Systems with Time-Delay

Based on a new linear, continuous and bounded operator (PGOPO), a more effective approach and optimal control algorithm than by the block-pulse functions and Walsh functions to design the linear servomechanism of time-varying systems with time-delay is proposed in the paper. By means of the operator, the differential equation is transferred to a more explicit algebraic form which is much easier than the numerical integration of nonlinear TPBVP derived from Pantryagin's maximum principle method. Furthermore, the method is established strictly based on the theory of convergence in the mean square and it is convenient and simple in computation. So the method can be applied to industry control and aeronautics and astronautics field which is frequently mixed with time varying and time delay. Some illustrative numerical examples are interpreted to support the technique.

A Hybrid Security Framework for Medical Image Communication

Authentication of the digital image has much attention for the digital revolution.Digital image authentication can be verified with image watermarking and image encryption schemes.These schemes are widely used to protect images against forgery attacks,and they are useful for protecting copyright and rightful ownership.Depending on the desirable applications,several image encryption and watermarking schemes have been proposed to moderate this attention.This framework presents a new scheme that combines a Walsh Hadamard Transform(WHT)-based image watermarking scheme with an image encryption scheme based on Double Random Phase Encoding(DRPE).First,on the sender side,the secret medical image is encrypted using DRPE.Then the encrypted image is watermarking based on WHT.The combination between watermarking and encryption increases the security and robustness of transmitting an image.The performance evaluation of the proposed scheme is obtained by testing Structural Similarity Index(SSIM),Peak Signal-to-Noise Ratio(PSNR),Normalized cross-correlation(NC),and Feature Similarity Index(FSIM).

NON-ORTHOGONAL P-WAVELET PACKETS ON THE HALF-LINE

In this paper, the notion of p-wavelet packets on the positive half-line P＋ is introduced. A new method for constructing non-orthogonal wavelet packets related to Walsh functions is developed by splitting the wavelet subspaces directly instead of using the lowpass and high-pass filters associated with the multiresolution analysis as used in the classical theory of wavelet packets. Further, the method overcomes the difficulty of constructing non-orthogonal wavelet packets of the dilation factor p 〉 2.

The Walsh Transform of a Class of Boolean Functions

The Walsh transform is an important tool to investigate cryptographic properties of Boolean functions.This paper is devoted to study the Walsh transform of a class of Boolean functions defined as g(x)=f(x)Tr^(n)_(1)(x)+h(x)Tr^(n)_(1)(δx),by making use of the known conclusions of Walsh transform and the properties of trace function,and the conclusion is obtained by generalizing an existing result.

Some classes of complete permutation polynomials over Fq

By using a powerful criterion for permutation polynomials, we give several classes of complete permutation polynomials over finite fields. First, two classes of complete permutation monomials whose exponents are of Niho type are presented. Second, for any odd prime p, we give a sufficient and necessary condition for a-1xdto be a complete permutation polynomial over Fp4 k, where d =(p4k-1)/(pk-1)+ 1 and a ∈ F*p4k. Finally, we present a class of complete permutation multinomials, which is a generalization of recent work.