As a with-carry analog (based on modular arithmetic) of the usual Walsh-Hadamard transform (WHT), arithmetic Walsh transform (AWT) has been used to obtain analogs of some properties of Boolean functions which are important in the design and analysis of cryptosystems. The existence of nonzero linear structure of Boolean functions is an important criterion to measure the weakness of these functions in their cryptographic applications. In this paper, we find more analogs of linear structures of Boolean functions from AWT. For some classes of n-variable Boolean functions f, we find necessary and sufficient conditions for the existence of an invariant linear structure and a complementary linear structure 1n of f. We abstract out a sectionally linear relationship between AWT and WHT of n-variable balanced Boolean functions f with linear structure 1n. This result show that AWT can characterize cryptographic properties of these functions as long as WHT can. In addition, for a diagonal Boolean function f, a recent result by Carlet and Klapper says that the AWT of f can be expressed in terms of the AWT of a diagonal Boolean function of algebraic degree at most 3 in a larger number of variables. We provide for the result a complete and more modular proof which works for both even and odd weights (of the parameter c in the Corollary 19 by Carlet and Klapper (DCC 73(2): 299-318, 2014).

In this letter, the interference cancellation technique is introduced to single carrier (SC) block transmission systems in sparse Rician frequency selective fading channels, and an effective equalizer is presented. Hard decision on the transmitted signal is made by commonly used SC equalizers, and every multipath signal can be constructed by the initial solution and channel state information. Then, final demodulation result is obtained by the line-of-sight component in the received signal which can be achieved by cancelling the other multipath signals in the received signal. The solution can be further used to construct the multipath signals allowing a multistage detector with higher performance to be realized. It is shown by Monte Carlo simulations in an SUI-5 channel that the new scheme offers dramatically higher performance than traditional equalization schemes.

Image boundary detection or image segmentation is an important step in image analysis. However, choosing appropriate parameters for boundary detection algorithms is necessary to achieve good boundary detection results. Image boundary detection fusion with unsupervised parameters can output a final consensus boundary, which is generally better than using unsupervised or supervised image boundary detection algorithms. In this study, we theoretically examine why image boundary detection fusion can work well and we propose a mixture model for image boundary detection fusion (MMIBDF) to achieve good consensus segmentation in an unsupervised manner. All of the segmentation algorithms are treated as new features and the segmentation results obtained by the algorithms are the values of the new features. The MMIBDF is designed to sample the boundary according to a discrete distribution. We present an inference method for MMIBDF and describe the corresponding algorithm in detail. Extensive empirical results demonstrate that MMIBDF significantly outperforms other image boundary detection fusion algorithms and the base image boundary detection algorithms according to most performance indices.