Based on a unified representation of generalized cyclotomic classes, every generalized cyclotomic sequence of order d over $Z_{p_{1}^{e_{1}}p_{2}^{e_{2}}cdots p_{r}^{e_{r}}}$ is shown to be a sum of d-residue sequences over $Z_{p_{s}^{e_{s}}}$ for $sin {1,2,cdots,r }$. For d=2, by the multi-rate approach, several generalized cyclotomic sequences are explicitly expressed by Legendre sequences, and their linear complexity properties are analyzed.

For an odd prime p and a positive integer r, new classes of binary sequences with period pr+1 are proposed from Euler quotients in this letter, which include several known classes of binary sequences derived from Fermat quotients and Euler quotients as special cases. The advantage of the new constructions is that they allow one to choose their support sets freely. Furthermore, with some constrains on the support set, the new sequences are proved to possess large linear complexities under the assumption of 2p-1 ≢ 1 mod p2.

Several models of feed-forward complex-valued neural networks have been proposed, and those with split and polar-represented activation functions have been mainly studied. Neural networks with split activation functions are relatively easy to analyze, but complex-valued neural networks with polar-represented functions have many applications but are difficult to analyze. In previous research, Nitta proved the uniqueness theorem of complex-valued neural networks with split activation functions. Subsequently, he studied their critical points, which caused plateaus and local minima in their learning processes. Thus, the uniqueness theorem is closely related to the learning process. In the present work, we first define three types of reducibility for feed-forward complex-valued neural networks with polar-represented activation functions and prove that we can easily transform reducible complex-valued neural networks into irreducible ones. We then prove the uniqueness theorem of complex-valued neural networks with polar-represented activation functions.

Non-orthogonal multiple access (NOMA) utilizing the power domain and advanced receiver has been considered as one promising multiple access technology for further cellular enhancements toward the 5th generation (5G) mobile communications system. Most of the existing investigations into NOMA focus on the combination of NOMA with orthogonal frequency division multiple access (OFDMA) for either downlink or uplink. In this paper, we investigate NOMA for uplink with single carrier-frequency division multiple access (SC-FDMA) being used. Differently from OFDMA, SC-FDMA requires consecutive resource allocation to a user equipment (UE) in order to achieve low peak to average power ratio (PAPR) transmission by the UE. Therefore, sophisticated designs of scheduling algorithm for NOMA with SC-FDMA are needed. To this end, this paper investigates the key issues of uplink NOMA scheduling such as UE grouping method and resource widening strategy. Because the optimal schemes have high computational complexity, novel schemes with low computational complexity are proposed for practical usage for uplink resource allocation of NOMA with SC-FDMA. On the basis of the proposed scheduling schemes, the performance of NOMA is investigated by system-level simulations in order to provide insights into the suitability of using NOMA for uplink radio access. Key issues impacting NOMA performance are evaluated and analyzed, such as scheduling granularity, UE number and the combination with fractional frequency reuse (FFR). Simulation results verify the effectiveness of the proposed algorithms and show that NOMA is a promising radio access technology for 5G systems.

The iterative random subdivision of rectangles is used as a generation model of networks in physics, computer science, and urban planning. However, these researches were independent. We consider some relations in them, and derive fundamental properties for the average lifetime depending on birth-time and the balanced distribution of rectangle faces.

Let r be an odd prime, such that r≥5 and r≠p, m be the order of r modulo p. Then, there exists a 2pth root of unity in the extension field Frm. Let G(x) be the generating polynomial of the considered quaternary sequences over Fq[x] with q=rm. By explicitly computing the number of zeros of the generating polynomial G(x) over Frm, we can determine the degree of the minimal polynomial, of the quaternary sequences which in turn represents the linear complexity. In this paper, we show that the minimal value of the linear complexity is equal to $ rac{1}{2}(3p-1) $ which is more than p, the half of the period 2p. According to Berlekamp-Massey algorithm, these sequences viewed as enough good for the use in cryptography.

In recent years, applications of complex-valued neural networks have become wide spread. Quaternions are an extension of complex numbers, and neural networks with quaternions have been proposed. Because quaternion algebra is non-commutative algebra, we can consider two orders of multiplication to calculate weighted input. However, both orders provide almost the same performance. We propose hybrid quaternionic Hopfield neural networks, which have both orders of multiplication. Using computer simulations, we show that these networks outperformed conventional quaternionic Hopfield neural networks in noise tolerance. We discuss why hybrid quaternionic Hopfield neural networks improve noise tolerance from the standpoint of rotational invariance.

The number of states is a very important matter for model checking approach in Petri net's analysis. We first gave a formal definition of state number calculation problem: For a Petri net with an initial state (marking), how many states does it have? Next we showed the problem cannot be solved in polynomial time for a popular subclass of Petri nets, known as free choice workflow nets, if P≠NP. Then we proposed a polynomial time algorithm to solve the problem by utilizing a representational bias called as process tree. We also showed effectiveness of the algorithm through an application example.

The linear complexity of binary sequences plays a fundamental part in cryptography. In the paper, we construct more general forms of generalized cyclotomic binary sequences with period 2pm+1qn+1. Furthermore, we establish the formula of the linear complexity of proposed sequences. The results reveal that such sequences with period 2pm+1qn+1 have a good balance property and high linear complexity.

Coordinated multi-point (CoMP) transmission and reception is a promising technique for interference mitigation in cellular systems. The scheduling algorithm for CoMP has a significant impact on the network processing complexity and performance. Performing exhaustive search permits centralized scheduling and thus the optimal global solution; however, it incurs a high level of computational complexity and may be impractical or lead to high cost as well as network instability. In order to provide a more realistic scheduling method while balancing performance and complexity, we propose a low complexity centralized scheduling scheme that adaptively selects users for single-cell transmission or different CoMP scheme transmission to maximize the system weighted sum capacity. We evaluate the computational complexity and system-level simulation performance in this paper. Compared to the optimal scheduling method with exhaustive search, the proposed scheme has a much lower complexity level and achieves near optimal performance.

In this paper, we explore possibilities and difficulties to prove super-quadratic formula size lower bounds from the following aspects. First, we consider recursive Boolean functions and prove their general formula size upper bounds. We also discuss recursive Boolean functions based on exact 2-bit functions. We show that their formula complexity are at least Ω(n2). Hence they can be candidate Boolean functions to prove super-quadratic formula size lower bounds. Next, we consider the reason of the difficulty of resolving the formula complexity of the majority function in contrast with the parity function. In particular, we discuss the structure of an optimal protocol partition for the Karchmer-Wigderson communication game.

Golf is a solitaire game, where the object is to move all cards from a 5×8 rectangular layout of cards to the foundation. A top card in each column may be moved to the foundation if it is either one rank higher or lower than the top card of the foundation. If no cards may be moved, then the top card of the stock may be moved to the foundation. We prove that the generalized version of Golf Solitaire is NP-complete.

Forty Thieves is a solitaire game with two 52-card decks. The object is to move all cards from ten tableau piles of four cards to eight foundations. Each foundation is built up by suit from ace to king of the same suit, and each tableau pile is built down by suit. You may move the top card from any tableau pile to a tableau or foundation pile, and from the stock to a foundation pile. We prove that the generalized version of Forty Thieves is NP-complete.

A processing system with multiple field programmable gate array (FPGA) cards is described. Each FPGA card can interconnect using six I/O (up, down, left, right, front, and back) terminals. The communication network among FPGAs is scalable according to user design. When the system operates multi-dimensional applications, transmission efficiency among FPGA improved through user-adjusted dimensionality and network topologies for different applications. We provide a fast and flexible circuit configuration method for FPGAs of a multi-dimensional FPGA array. To demonstrate the effectiveness of the proposed method, we assess performance and power consumption of a circuit that calculated 3D Poisson equations using the finite difference method.

We fabricated organic field-effect transistors (OFETs) having a thin layer of molybdenum trioxide (MoO$_3$), a Lewis acid, and evaluated their electrical characteristics. The insertion of a thin MoO$_3$ layer reduces the on/off ratio but improves the apparent mobility of the charge carriers. To identify the dominant mechanism responsible for this effect, we characterized devices having a 69-nm-thick pentacene layer with a 1-nm-thick MoO$_3$ layer either between the gold source and the drain electrodes or only directly under these electrodes. The former device exhibited a low on/off ratio, whereas the latter device exhibited an on/off ratio comparable to those of conventional pentacene OFETs without a thin MoO$_3$ layer, suggesting that the formation of charge-transfer (CT) complexes immediately above the conduction channel is the critical mechanism. CT complexes at the pentacene/MoO$_3$ interface immediately above the conduction channel contribute to the formation of an effective channel for off-currents as well as drain currents. Moreover, we also attempted to improve the on/off ratio by using a cloth to rub the surface of a thin MoO$_3$ layer immediately above the conduction channel to create what we believe to be a profile with abrupt changes in height in the direction of the drain current conduction in OFETs. Consequently, it was found that such a rubbed MoO$_3$ layer had a surface with a scratched pattern, and the on/off ratio of the OFET was improved, indicating that controlling the CT complex formation by patterning a MoO$_3$ layer can reduce the off-current in OFETs having a pentacene/MoO$_3$ active layer.

In several important applications, we often encounter with the computation of a Toeplitz matrix vector product (TMVP). In this work, we propose a k-way splitting method for a TMVP over any field F, which is a generalization of that over GF(2) presented by Hasan and Negre. Furthermore, as an application of the TMVP method over F, we present the first subquadratic space complexity multiplier over any finite field GF(pn) defined by an irreducible trinomial.

The stability theory of stream ciphers plays an important role in designing good stream cipher systems. Two algorithms are presented, to determine the optimal shift and the minimum linear complexity of the sequence, that differs from a given sequence over Fq with period qn-1 by one digit. We also describe how the linear complexity changes with respect to one digit differing from a given sequence.

The maximization of non-Gaussianity is an effective approach to achieve the complex independent component analysis (ICA) problem. However, the traditional complex maximization of non-Gaussianity (CMN) algorithm does not consider the influence of noise. In this letter, a modification of the fixed-point algorithm is proposed for more practical occasions of the complex noisy ICA model. Simulations show that the proposed method demonstrates significantly improved performance over the traditional CMN algorithm in the noisy ICA model when the sample size is sufficient.

The development of high data rate wireless communications systems using Multiple Input — Multiple Output (MIMO) antenna techniques requires detectors with reduced complexity and good Bit Error Rate (BER) performance. In this paper, we present the Semi-fixed Complexity Sphere Decoder (SCSD), which executes the process of detection in MIMO systems with a significantly lower computation cost than the high-performance/reduced-complexity detectors: Sphere Decoder (SD), K-best, Fixed Complexity Sphere Decoder (FSD) and Adaptive Set Partitioning (ASP). Simulation results show that when the Signal-to-Noise Ratio (SNR) is less than 15dB, the SCSD reduces the complexity by up to 90% with respect to SD, up to 60% with respect to K-best or ASP and by up to 90% with respect to FSD. In the proposed algorithm, the BER performance does not show significant degradation and therefore, can be considered as a complexity reduction scheme suitable for implementing in MIMO detectors.

In this paper, an adaptive expansion strategy (AES) is proposed for multiple-input/multiple-output (MIMO) detection in the presence of circular signals. By exploiting channel properties, the AES classifies MIMO channels into three types: excellent, average and deep fading. To avoid unnecessary branch-searching, the AES adopts single expansion (SE), partial expansion (PE) and full expansion (FE) for excellent channels, average channels and deep fading channels, respectively. In the PE, the non-circularity of signal is exploited, and the widely linear processing is extended from non-circular signals to circular signals by I (or Q) component cancellation. An analytical performance analysis is given to quantify the performance improvement. Simulation results show that the proposed algorithm can achieve quasi-optimal performance with much less complexity (hundreds of flops/symbol are saved) compared with the fixed-complexity sphere decoder (FSD) and the sphere decoder (SD).