Jacobi sequences have good cryptography properties. Li et al. [X. Li et al., Linear Complexity of a New Generalized Cyclotomic Sequence of Order Two of Length pq*, IEICE Trans. Fundamentals, vol.E96-A, no.5, pp.1001-1005, 2013] defined a new modified Jacobi sequence of order two and got its linear complexity. In this corresponding, we determine the linear complexity and minimal polynomials of the new modified Jacobi sequence of order d. Our results show that the sequence is good from the viewpoint of linear complexity.

Underfill materials are used in a packaging of millimeter wave IC. However, there are few reports for dielectric properties of underfill materials in millimeter wave region. A cut-off circular waveguide method is one of a powerful technique to evaluate precisely complex permittivity in millimeter wave region. This method may be useful not only for low-loss materials, but also for mid-loss ones with loss tangent of 10$^{-2}$ order. In this paper, an evaluation technique based on the cut-off circular waveguide method is presented to measure mid-loss underfill materials. As a result, the relative permittivity $arepsilon_{r}$ and the loss tangent tan$delta$ are in the range of 2.8$sim $3.4 and (1.0$sim$1.6)$ imes10^{-2}$, respectively. Also, the measurement precision is 2.3% for $arepsilon_{r} approx 3$ and 40% for tan$delta approx 10^{-2}$.

With the phenomenal explosion in online services, social networks are becoming an emerging ubiquitous platform for numerous services where service consumers require the selection of trustworthy service providers before invoking services with the help of other intermediate participants. Under this circumstance, evaluation of the trustworthiness of the service provider along the social trust paths from the service consumer to the service provider is required and to this end, selection of the optimal social trust path (OSTP) that can yield the most trustworthy evaluation result is a pre-requisite. OSTP selection with multiple quality of trust (QoT) constraints has been proven to be NP-Complete. Heuristic algorithms with polynomial and pseudo-polynomial-time complexities are often used to deal with this problem. However, existing solutions cannot guarantee the search efficiency, that is, they have difficulty in avoiding suboptimal solutions during the search process. Quantum annealing uses delocalization and tunneling to avoid local minima without sacrificing execution time. Several recent studies have proven that it is a promising way to tackle many optimization problems. In this paper, we propose a novel quantum annealing based OSTP selection algorithm (QA_OSTP) for large-scale complex social networks. Experiments show that QA_OSTP has better performance than its heuristic counterparts.

Recently the word-based stream ciphers have been the subject of a considerable amount of research. The theory of such stream ciphers requires the study of the complexity of a multisequence. Let S1, S2, . . . , Sm be m N-ary sequences of period T, i.e., a multisequence. The relationship between the joint N-adic complexity and the number of the nonzero columns of the generalized Fourier transform for the N-ary multisequence is determined which generalizes the well-known result about the joint linear complexity and the generalized Fourier transform for a multisequence to the case of the joint N-adic complexity.

Visual quality evaluation is crucially important for various video and image processing systems. Traditionally, subjective image quality assessment (IQA) given by the judgments of people can be perfectly consistent with human visual system (HVS). However, subjective IQA metrics are cumbersome and easily affected by experimental environment. These problems further limits its applications of evaluating massive pictures. Therefore, objective IQA metrics are desired which can be incorporated into machines and automatically evaluate image quality. Effective objective IQA methods should predict accurate quality in accord with the subjective evaluation. Motivated by observations that HVS is highly adapted to extract irregularity information of textures in a scene, we introduce multifractal formalism into an image quality assessment scheme in this paper. Based on multifractal analysis, statistical complexity features of nature images are extracted robustly. Then a novel framework for image quality assessment is further proposed by quantifying the discrepancies between multifractal spectrums of images. A total of 982 images are used to validate the proposed algorithm, including five type of distortions: JPEG2000 compression, JPEG compression, white noise, Gaussian blur, and Fast Fading. Experimental results demonstrate that the proposed metric is highly effective for evaluating perceived image quality and it outperforms many state-of-the-art methods.

There have been many matching pursuit algorithms (MPAs) which handle the sparse signal recovery problem, called compressed sensing (CS). In the MPAs, the correlation step makes a dominant computational complexity. In this paper, we propose a new fast correlation method for the MPA when we use partial Fourier sensing matrices and partial Hadamard sensing matrices which are widely used as the sensing matrix in CS. The proposed correlation method can be applied to almost all MPAs without causing any degradation of their recovery performance. Also, the proposed correlation method can reduce the computational complexity of the MPAs well even though there are restrictions depending on a used MPA and parameters.

Complex-valued Hopfield associative memory (CHAM) is one of the most promising neural network models to deal with multilevel information. CHAM has an inherent property of rotational invariance. Rotational invariance is a factor that reduces a network's robustness to noise, which is a critical problem. Here, we proposed complex-valued bipartite auto-associative memory (CBAAM) to solve this reduction in noise robustness. CBAAM consists of two layers, a visible complex-valued layer and an invisible real-valued layer. The invisible real-valued layer prevents rotational invariance and the resulting reduction in noise robustness. In addition, CBAAM has high parallelism, unlike CHAM. By computer simulations, we show that CBAAM is superior to CHAM in noise robustness. The noise robustness of CHAM decreased as the resolution factor increased. On the other hand, CBAAM provided high noise robustness independent of the resolution factor.

The k-error linear complexity of periodic sequences is an important security index of stream cipher systems. By using an interesting decomposing approach, we investigate the intrinsic structure for the set of 2n-periodic binary sequences with fixed complexity measures. For k ≤ 4, we construct the complete set of error vectors that give the k-error linear complexity. As auxiliary results we obtain the counting functions of the k-error linear complexity of 2n-periodic binary sequences for k ≤ 4, as well as the expectations of the k-error linear complexity of a random sequence for k ≤ 3. Moreover, we study the 2t-error linear complexity of the set of 2n-periodic binary sequences with some fixed linear complexity L, where t < n-1 and the Hamming weight of the binary representation of 2n-L is t. Also, we extend some results to pn-periodic sequences over Fp. Finally, we discuss some potential applications.

In this paper, the linear complexity and minimal polynomials of Legendre sequences over Fq have been calculated, where q = pm and p is a prime number. Our results show that Legendre sequences have high linear complexity over Fq for a large part of prime power number q so that they can resist the linear attack method.

In this paper, a novel hybrid technique for analyzing complex antennas around the coated object is proposed, which is termed as “iterative vector fields with Physical Optics (PO)”. A closed box is used to enclose the antennas and the complex field vectors on the box' surfaces can then be obtained using Huygens principle. The equivalent electromagnetic currents on Huygens surfaces are computed by Higher-order Method of Moments (HOB-MoM) and the fields scattered from the coated object are calculated by PO method. In addition, the parallel technique based on Message Passing Interface (MPI) and Scalable Linear Algebra Package (ScaLAPACK) is employed so as to accelerate the computation. Numerical examples are presented to validate and to show the effectiveness of the proposed method on solving the practical engineering problem.

In compressed sensing, the design of the measurement matrix is a key work. In order to achieve a more precise reconstruction result, the columns of the measurement matrix should have better orthogonality or linear incoherence. A random matrix, like a Gaussian random matrix (GRM), is commonly adopted as the measurement matrix currently. However, the columns of the random matrix are only statistically-orthogonal. By substituting an orthogonal basis into the random matrix to construct a semi-random measurement matrix and by optimizing the mutual coherence between dictionary columns to approach a theoretical lower bound, the linear incoherence of the measurement matrix can be greatly improved. With this optimization measurement matrix, the signal can be reconstructed from its measures more precisely.

A cooperating system of finite automata (CS-FA) has more than one finite automata (FA's) and an input tape. These FA's operate independently on the input tape and can communicate with each other on the same cell of the input tape. For each k ≥ 1, let L[CS-1DFA(k)] (L[CS-1UFA(k)]) be the class of sets accepted by CS-FA's with k one-way deterministic finite automata (alternating finite automata with only universal states). We show that L[CS-1DFA(k+1)] - L[CS-1UFA(k)] ≠ ∅ and L[CS-1UFA(2)] - ∪1≤k<∞L[CS-1DFA(k)] ≠ ∅.

In this paper, we show a connection between #P and computing the (real) value of the high order derivative at the origin. Consider, as a problem instance, an integer b and a sufficiently often differentiable function F(x) that is given as a string. Then we consider computing the value F(b)(0) of the b-th derivative of F(x) at the origin. By showing a polynomial as an example, we show that we have FP = #P if we can compute log 2F(b)(0) up to certain precision. The previous statement holds even if F(x) is limited to a function that is analytic at any x ∈ R. It implies the hardness of computing the b-th value of a number sequence from the closed form of its generating function.

In the paper [4], the authors generalized the Cipolla-Lehmer method [2][5] for computing square roots in finite fields to the case of r-th roots with r prime, and compared it with the Adleman-Manders-Miller method [1] from the experimental point of view. In this paper, we compare these two methods from the theoretical point of view.

In this paper we apply angle recoding to the CORDIC-based processing elements in a scalable architecture for complex matrix inversion. We extend the processing elements from the scalable real matrix inversion architecture to the complex domain and obtain the novel scalable complex matrix inversion architecture, which can significantly reduce computational complexity. We rearrange the CORDIC elements to make one half of the processing elements simple and compact. For the other half of the processing elements, the efficient use of angler recoding reduces the number of microrotation steps of the CORDIC elements to 3/4. Consequently, only 3 CORDIC elements are required for the processing elements with full utilization.

Pseudo-random sequences with high linear complexity play important roles in many domains. We give linear complexity of generalized cyclotomic quaternary sequences with period pq over Z4 via the weights of its Fourier spectral sequence. The results show that such sequences have high linear complexity.

High Efficiency Video Coding (HEVC) is the latest video coding standard that is supported by JCT-VC. In this letter, an encoding algorithm for early termination of Coding Unit (CU) and Prediction Unit (PU) based on the texture direction is proposed for the HEVC intra prediction. Experimental results show that the proposed algorithm provides an average 40% total encoding time reduction with the negligible loss of rate-distortion.

We determine the linear complexity of binary sequences derived from the polynomial quotient modulo p defined by $F(u)equiv rac{f(u)-f_p(u)}{p} ~(mod~ p), qquad 0 le F(u) le p-1,~uge 0,$ where fp(u)≡f(u) (mod p), for general polynomials $f(x)in mathbb{Z}[x]$. The linear complexity equals to one of the following values {p2-p,p2-p+1,p2-1,p2} if 2 is a primitive root modulo p2, depending on p≡1 or 3 modulo 4 and the number of solutions of f'(u)≡0 (mod) p, where f'(x) is the derivative of f(x). Furthermore, we extend the constructions to d-ary sequences for prime d|(p-1) and d being a primitive root modulo p2.

In this paper, we focus on the multi-way relaying channel where K users wish to exchange information with each other within two phases. Precoding at each user and the relay is carefully constructed to ensure that the signals from the same user pair are grouped together and cross-pair interference can be cancelled. Reliable detection is challenging at the relay since the observation constellation is no longer one of the regular ones, due to the fact that a relay observation is the superposition of the messages from one of the $rac{1}{2}K(K-1)$ user pairs. When the trellis coded modulation is used at each node, a simple constellation mapping function and a reduced-states decoding scheme can be applied at the relay, which result in much lower complexity. Furthermore, a modified version of the decoding method is also developed which is called the re-encoding-avoidance scheme at the relay. Monte-Carlo simulation results are provided to demonstrate the performance of the proposed scheme.

Blind source separation is a technique that can separate sound sources without such information as source location, the number of sources, and the utterance content. Multi-channel source separation using many microphones separates signals with high accuracy, even if there are many sources. However, these methods have extremely high computational complexity, which must be reduced. In this paper, we propose a computational complexity reduction method for blind source separation based on frequency domain independent component analysis (FDICA) and examine temporal data that are effective for source separation. A frame with many sound sources is effective for FDICA source separation. We assume that a frame with a low kurtosis has many sound sources and preferentially select such frames. In our proposed method, we used the log power spectrum and the kurtosis of the magnitude distribution of the observed data as selection criteria and conducted source separation experiments using speech signals from twelve speakers. We evaluated the separation performances by the signal-to-interference ratio (SIR) improvement score. From our results, the SIR improvement score was 24.3dB when all the frames were used, and 23.3dB when the 300 frames selected by our criteria were used. These results clarified that our proposed selection criteria based on kurtosis and magnitude is effective. Furthermore, we significantly reduced the computational complexity because it is proportional to the number of selected frames.