In this letter, a physical-layer network coding (PNC) scheme based on continuous phase modulation (CPM) signal using the titled-phase model, i.e., TIP-CPM-PNC, is presented, and the combined titled-phase state trellis for the superimposed CPM signal in TIP-CPM-PNC is discussed. Simulation results show that the proposed scheme with low decoding complexity can achieve the same error performance as CPM-PNC using the traditional-phase model.

In the past two decades, many generalized cyclotomic sequences have been constructed and they have been used in cryptography and communication systems for their high linear complexity and low autocorrelation. But there are a few of papers focusing on the 2-adic complexities of such sequences. In this paper, we first give a property of a class of Gaussian periods based on Whiteman's generalized cyclotomic classes of order 4. Then, as an application of this property, we study the 2-adic complexity of a class of Whiteman's generalized cyclotomic sequences constructed from two distinct primes p and q. We prove that the 2-adic complexity of this class of sequences of period pq is lower bounded by pq-p-q-1. This lower bound is at least greater than one half of its period and thus it shows that this class of sequences can resist against the rational approximation algorithm (RAA) attack.

Pseudorandom number generators are required to generate pseudorandom numbers which have good statistical properties as well as unpredictability in cryptography. An m-sequence is a linear feedback shift register sequence with maximal period over a finite field. M-sequences have good statistical properties, however we must nonlinearize m-sequences for cryptographic purposes. A geometric sequence is a sequence given by applying a nonlinear feedforward function to an m-sequence. Nogami, Tada and Uehara proposed a geometric sequence whose nonlinear feedforward function is given by the Legendre symbol, and showed the period, periodic autocorrelation and linear complexity of the sequence. Furthermore, Nogami et al. proposed a generalization of the sequence, and showed the period and periodic autocorrelation. In this paper, we first investigate linear complexity of the geometric sequences. In the case that the Chan-Games formula which describes linear complexity of geometric sequences does not hold, we show the new formula by considering the sequence of complement numbers, Hasse derivative and cyclotomic classes. Under some conditions, we can ensure that the geometric sequences have a large linear complexity from the results on linear complexity of Sidel'nikov sequences. The geometric sequences have a long period and large linear complexity under some conditions, however they do not have the balance property. In order to construct sequences that have the balance property, we propose interleaved sequences of the geometric sequence and its complement. Furthermore, we show the periodic autocorrelation and linear complexity of the proposed sequences. The proposed sequences have the balance property, and have a large linear complexity if the geometric sequences have a large one.

In this paper, we devise low-complexity uplink detection algorithms for Massive MIMO systems. We treat the uplink detection as an ill-posed problem and adopt the Landweber Method to solve it. In order to reduce the computational complexity and increase the convergence rate, we propose improved Landweber Method with optimal relax factor (ILM-O) algorithm. In addition, to reduce the order of Landweber Method by introducing a set of coefficients, we propose reduced order Landweber Method (ROLM) algorithm. An analysis on the convergence and the complexity is provided. Numerical results demonstrate that the proposed algorithms outperform the existing algorithm.

By exploiting the inherent sparsity of wireless channels, the channel estimation in an orthogonal frequency division multiplexing (OFDM) system can be cast as a compressed sensing (CS) problem to estimate the channel more accurately. Practically, matching pursuit algorithms such as orthogonal matching pursuit (OMP) are used, where path delays of the channel is guessed based on correlation values for every quantized delay with residual. This full search approach requires a predefined grid of delays with high resolution, which induces the high computational complexity because correlation values with residual at a huge number of grid points should be calculated. Meanwhile, the correlation values with high resolution can be obtained by interpolation between the correlation values at a low resolution grid. Also, the interpolation can be implemented with a low pass filter (LPF). By using this fact, in this paper we substantially reduce the computational complexity to calculate the correlation values in channel estimation using CS.

In many communications applications, maximum-likelihood decoding reduces to solving an integer least-squares problem, which is NP-hard in the worst case. It has recently been shown that over a wide range of dimensions and SNRs, the branch and bound (BB) algorithm can be used to find the exact solution with an expected complexity that is roughly cubic in the dimension of the problem. However, the computational complexity becomes prohibitive if the SNR is too low and/or the dimension of the problem is too large. The dichotomous coordinate descent (DCD) algorithm provides low complexity, but its detection performance is not as good as that of the BB detector. Two methods are developed to bound the optimal detector cost to reduce the complexity of BB in this paper. These methods are DCD-based detectors for MIMO and multiuser detection in the scenario of a large number of transmitting antennas/users. First, a combined detection technique based on the BB and DCD algorithms is proposed. The technique maintains the advantages of both algorithms and achieves a good trade-off between performance and complexity compared to using only the BB or DCD algorithm. Second, since the first feasible solution obtained from the BB search is the solution of the decorrelating decision feedback (DF) method and because DCD results in better accuracy than the decorrelating DF solution, we propose that the first feasible solution of the BB algorithm be obtained by the box-constrained DCD algorithm rather than the decorrelating DF detector. This method improves the precision of the initial solution and identifies more branches that can be eliminated from the search tree. The results show that the DCD-based BB detector provides optimal detection with reduced worst-case complexity compared to that of the decorrelating DF-based BB detector.

We consider a device-to-device (D2D) underlaid cellular network where D2D communications are allowed to share the same radio spectrum with cellular uplink communications for improving spectral efficiency. However, to protect the cellular uplink communications, the interference level received at a base station (BS) from the D2D communications needs to be carefully maintained below a certain threshold, and thus the BS coordinates the transmit power of the D2D links. In this paper, we investigate on-off power control for the D2D links, which is known as a simple but effective technique due to its low signaling overhead. We first investigate the optimal on-off power control algorithm to maximize the sum-rate of the D2D links, while satisfying the interference constraint imposed by the BS. The computational complexity of the optimal algorithm drastically increases with D2D link number. Thus, we also propose an on-off power control algorithm to significantly reduce the computational complexity, compared to the optimal on-off power control algorithm. Extensive simulations validate that the proposed algorithm significantly reduces the computational complexity with a marginal sum-rate offset from the optimal algorithm.

The energy of a threshold circuit C is defined to be the maximum number of gates outputting ones for an input assignment, where the maximum is taken over all the input assignments. In this paper, we study computational power of threshold circuits of energy at most two. We present several results showing that the computational power of threshold circuits of energy one and the counterpart of energy two are remarkably different. In particular, we give an explicit function which requires an exponential size for threshold circuits of energy one, but is computable by a threshold circuit of size just two and energy two. We also consider MOD functions and Generalized Inner Product functions, and show that these functions also require exponential size for threshold circuits of energy one, but are computable by threshold circuits of substantially less size and energy two.

We prove generalization error bounds of classes of low-rank matrices with some norm constraints for collaborative filtering tasks. Our bounds are tighter, compared to known bounds using rank or the related quantity only, by taking the additional L1 and L∞ constraints into account. Also, we show that our bounds on the Rademacher complexity of the classes are optimal.

The k-error linear complexity of a sequence is a fundamental concept for assessing the stability of the linear complexity. After computing the k-error linear complexity of a sequence, those bits that cause the linear complexity reduced also need to be determined. For binary sequences with period 2pn, where p is an odd prime and 2 is a primitive root modulo p2, we present an algorithm which computes the minimum number k such that the k-error linear complexity is not greater than a given constant c. The corresponding error sequence is also obtained.

Response property is a kind of liveness property. Response property problem is defined as follows: Given two activities α and β, whenever α is executed, is β always executed after that? In this paper, we tackled the problem in terms of Workflow Petri nets (WF-nets for short). Our results are (i) the response property problem for acyclic WF-nets is decidable, (ii) the problem is intractable for acyclic asymmetric choice (AC) WF-nets, and (iii) the problem for acyclic bridge-less well-structured WF-nets is solvable in polynomial time. We illustrated the usefulness of the procedure with an application example.

In wireless communication systems, OFDM technology is a communication method that can yield high data rates. However, OFDM systems suffer high PAPR values due to the use of many of subcarriers. The SLM and the PTS technique were proposed to solve the PAPR problem in OFDM systems. However, these approaches have the disadvantage of having high complexity. This paper proposes a method which has lower complexity than the conventional PTS method but has less performance degradation.

A family of quaternary sequences over Z4 is defined based on the Ding-Helleseth generalized cyclotomic classes modulo pq for two distinct odd primes p and q. The linear complexity is determined by computing the defining polynomial of the sequences, which is in fact connected with the discrete Fourier transform of the sequences. The results show that the sequences possess large linear complexity and are “good” sequences from the viewpoint of cryptography.

In this paper, we present a new three-way split formula for binary polynomial multiplication (PM) with five recursive multiplications. The scheme is based on a recently proposed multievaluation and interpolation approach using field extension. The proposed PM formula achieves the smallest space complexity. Moreover, it has about 40% reduced time complexity compared to best known results. In addition, using developed techniques for PM formulas, we propose a three-way split formula for Toeplitz matrix vector product with five recursive products which has a considerably improved complexity compared to previous known one.

In this paper, we propose a low-complexity widely-linear minimum mean square error (WL-MMSE) signal detection based on the Chebyshev polynomials accelerated symmetric successive over relaxation (SSORcheb) algorithm for uplink (UL) over-loaded large-scale multiple-input multiple-output (MIMO) systems. The technique of utilizing Chebyshev acceleration not only speeds up the convergence rate significantly, and maximizes the data throughput, but also reduces the cost. By utilizing the random matrix theory, we present good estimates for the Chebyshev acceleration parameters of the proposed signal detection in real large-scale MIMO systems. Simulation results demonstrate that the new WL-SSORcheb-MMSE detection not only outperforms the recently proposed linear iterative detection, and the optimal polynomial expansion (PE) WL-MMSE detection, but also achieves a performance close to the exact WL-MMSE detection. Additionally, the proposed detection offers superior sum rate and bit error rate (BER) performance compared to the precision MMSE detection with substantially fewer arithmetic operations in a short coherence time. Therefore, the proposed detection can satisfy the high-density and high-mobility requirements of some of the emerging wireless networks, such as, the high-mobility Internet of Things (IoT) networks.

A Tikhonov regularized RLS algorithm with an exponential weighting factor, i.e., a leaky RLS (LRLS) algorithm was proposed by the author. A quadratic version of the LRLS algorithm also exists in the literature of adaptive filters. In this letter, a cubic version of the LRLS filter which is computationally efficient is proposed when the length of the adaptive filter is short. The proposed LRLS filter includes only a divide per iteration although its multiplications and additions increase in number. Simulation results show that the proposed LRLS filter is faster for its short length than the existing quadratic version of the LRLS filter.

Multichannel speech enhancement systems (MSES') have been widely utilized for diverse types of speech interface applications. A state-of-the-art MSES primarily utilizes multichannel minima-controlled recursive averaging for noise estimations and a parameterized multichannel Wiener filter for noise reduction. Many MSES' are implemented in the frequency domain, but they are computationally burdensome due to the numerous complex matrix operations involved. In this paper, a novel MSES intended to reduce the computational complexity with improved performance is proposed. The proposed system is implemented in the mel-filterbank domain using a frequency-averaging technique. Through a performance evaluation, it is verified that the proposed mel-filterbank MSES achieves improvements in the perceptual speech quality with a reduced level of computation compared to a conventional MSES.

A fast parameter estimation method with a coarse estimation and a fine estimation for polyphase P coded signals is proposed. For a received signal with N sampling points, the proposed method has an improved performance when the signal-to-noise ratio (SNR) is larger than 2dB and a lower computational complexity O(N logs N) compared with the latest time-frequency rate estimation method whose computational complexity is O(N2).

Pseudorandom number generators have been widely used in Monte Carlo methods, communication systems, cryptography and so on. For cryptographic applications, pseudorandom number generators are required to generate sequences which have good statistical properties, long period and unpredictability. A Dickson generator is a nonlinear congruential generator whose recurrence function is the Dickson polynomial. Aly and Winterhof obtained a lower bound on the linear complexity profile of a Dickson generator. Moreover Vasiga and Shallit studied the state diagram given by the Dickson polynomial of degree two. However, they do not specify sets of initial values which generate a long period sequence. In this paper, we show conditions for parameters and initial values to generate long period sequences, and asymptotic properties for periods by numerical experiments. We specify sets of initial values which generate a long period sequence. For suitable parameters, every element of this set occurs exactly once as a component of generating sequence in one period. In order to obtain sets of initial values, we consider a logistic generator proposed by Miyazaki, Araki, Uehara and Nogami, which is obtained from a Dickson generator of degree two with a linear transformation. Moreover, we remark on the linear complexity profile of the logistic generator. The sets of initial values are described by values of the Legendre symbol. The main idea is to introduce a structure of a hyperbola to the sets of initial values. Our results ensure that generating sequences of Dickson generator of degree two have long period. As a consequence, the Dickson generator of degree two has some good properties for cryptographic applications.

Inter-switch networks for HPC systems and data-centers can be improved by applying random shortcut topologies with a reduced number of hops. With minimal routing in such networks; however, deadlock-freedom is not guaranteed. Multiple Virtual Channels (VCs) are efficiently used to avoid this problem. However, previous works do not provide good trade-offs between the number of required VCs and the time and memory complexities of an algorithm. In this work, a novel and fast algorithm, named ACRO, is proposed to endorse the arbitrary routing functions with deadlock-freedom, as well as consuming a small number of VCs. A heuristic approach to reduce VCs is achieved with a hash table, which improves the scalability of the algorithm compared with our previous work. Moreover, experimental results show that ACRO can reduce the average number of VCs by up to 63% when compared with a conventional algorithm that has the same time complexity. Furthermore, ACRO reduces the time complexity by a factor of O(|N|⋅log|N|), when compared with another conventional algorithm that requires almost the same number of VCs.