Let n ≥ 3 be an odd integer,d1=3n-1/2-1, d2=3n-2 andube an element of the finite field F3n. This paper shows thatfu(x)=uxd1+xd2is an almost perfect nonlinear (APN) function on F3n if and only if χ(u+1)= χ(u-1)=χ(u), where χ(∙) denotes the quadratic character of F3n. This settles the open problem raised by Ness and Helleseth in IEEE Trans. Inf. Theory 53(7): 2581-2586, 2007, where only the sufficiency part of the result was proved. Furthermore, we investigate the differential spectra offu(x)for elements u satisfying χ(u+1)=χ(u-1) and express them in terms of several quadratic character sums of cubic polynomials.

Abstract Thanks for its powerful feature extraction capability and unprecedented success in computer vision and language processing tasks, deep learning (DL) has also been applied in recent years to wireless communications. However, DL models are proved to be inherently vulnerable to adversarial perturbations: carefully crafted perturbations that appear imperceptible but can fool the models to induce misclassification. Existing researches in wireless communications employ the gradient‐based or optimization based methods, for example, FGSM, PGD and iterative FGSM, to craft input‐dependent adversarial perturbations. However, these methods have a high computational complexity and the perturbations they craft cannot be readily applied to fool DL‐based algorithms in wireless communications. In this paper, the efficient generation of universal (input‐agnostic) adversarial perturbations (UAPs) used to attack DL‐based modulation classification algorithms is studied. Communication signals exhibit unique characteristics, for example, received modulated signals after transmitting through noisy channels are densely distributed around the modulation constellation points. In this work, the authors have proposed, by making use of this unique characteristics, a generative network to model the distribution of adversarial perturbations for high‐efficiency generation of UAPs, which can fool the DL‐based modulation classification algorithms for most inputs. Instead of attacking all regions of modulated signals, attention mechanisms are introduced in generative network design that enables the perturbations to be concentrated around the constellation points. In this way, a higher attack efficiency and a lower perceptibility are achieved by crafting UAPs with smooth variations and more focused attack. In addition, a diversity term is included in loss function to help capture a wide range distribution of adversary perturbations that will help the generation of more diverse adversary perturbations. Once trained, the generative network can construct with ease a large number of UAPs with some favorable features, which will benefit more efficient adversarial attack and faster adversarial training. Experimental results show the superiority of our proposed method in terms of attack efficiency, imperceptibility and diversity over existing methods.

How to achieve a high transmission rate at a low cost of energy consumption in a wide range of channel variations is a critical challenge in Internet of Things (IoT) applications. In this article, a rateless 16 quadrature amplitude modulation (R-16QAM) scheme for IoT uplink communications is proposed to deal with this problem. The R-16QAM transmitter consists of an encoder, a random bit selector, and a tailored modulation mapper. Different from the sequential bits selection and Gary mapping in conventional 16QAM modulation, bits are randomly selected and mapped into a 16QAM symbol by a weighted summation of selected bits in R-16QAM. The random bits selection introduces correlation among modulated symbols, enabling the transmitter to work in a rateless manner, i.e., the transmitter keeps generating and sending R-16QAM symbols until a feedback of successful decoding is received from the receiver. It means that the number of symbols transmitted varies with channel variations. In this way, the proposed R-16QAM can automatically adjust to channel conditions and work well in a wide range of channel conditions. The weighted-summation mapping can be illustrated by a “Tanner graph,” based on which we develop a low complexity iterative demodulation algorithm to improve receiver performance. The simulations show that compared with narrow band Internet of Things (NB-IoT) standard and Turbo coded light-weight rate compatible modulation (TLRCM) for IoT uplink communications, the proposed R-16QAM scheme can consistently achieve a lower energy consumption in a signal-to-noise-ratio (SNR) range of −10–15 dB. Moreover, it can achieve a maximum transmission throughput of 3.96 bits/s/Hz at SNR=15 dB while only 0.66 and 1.7 bits/s/Hz are achieved in NB-IoT and TLRCM, respectively. These advantages enable the proposed R-16QAM scheme to be particularly suitable to IoT application scenarios where nodes work with limit energy resources under a large range of channel variations.

It is critical to lower the power consumption of battery powered nodes in Internet-of-Things (IoT) applications while maintaining a high transmission throughput. In this article, a novel turbo coded lightweight rate compatible modulation (TLRCM) with a simple weight set {±1} is proposed for IoT uplink transmission. Unlike narrowband IoT (NB-IoT) standard where the whole data block will be retransmitted repeatedly until the data are recovered successfully, the proposed TLRCM works in a rateless manner and can achieve a smooth rate adaptation to channel variations, reducing the number of symbols to be retransmitted. Thus, TLRCM can significantly reduce the power consumption of IoT device and improve transmission throughput. To reduce computational complexity, a 1-b subtraction and memory reading algorithm, which can be easily implemented in limited computing capability IoT devices, is proposed for the generation of TLRCM symbols. In addition, an iterative algorithm with significantly reduced complexity is proposed for TLRCM demodulation. Moreover, the reliable soft information from the output of TLRCM demodulator enables a fast convergence of Turbo codes decoding. The simulation results show that compared with the repetition transmission scheme in NB-IoT standard, the proposed TLRCM can reduce by over 37% the average transmission power consumption while maintaining a high throughput of transmission in both Gaussian channels and fading channels. The uniqueness of low-power consumption, high throughput transmission, and low-complexity implementation enables the proposed TLRCM to be a potential technique for IoT applications.

The 2-body correlation function (2-BCF) is a group of statistical measurements that found applications in many scientific domains. One type of 2-BCF named the Spatial Distance Histogram (SDH) is of vital importance in describing the physical features of natural systems. While a naïve way of computing SDH requires quadratical time, efficient algorithms based on resolving nodes in spatial trees have been developed. A key decision in the design of such algorithms is to choose a proper underlying data structure: our previous work utilizes quad-tree (oct-tree for 3D data) and, in this paper, we study a kd-tree-based solution. Although it is easy to see that both implementations have the same time complexity O(N2d−1d)⁠, where d is the number of dimensions of the dataset, a thorough comparison of their actual running time under different scenarios is conducted. In particular, we present an analytical model to rigorously quantify the running time of dual-tree algorithms. Our analysis suggests that the kd-tree-based implementation outperforms the quad-/oct-tree solution under a wide range of data sizes and query parameters. Specifically, such performance advantage is shown as a speedup up to 1.23× over the quad-tree algorithm for 2D data, and 1.39× over the oct-tree for 3D data, respectively. Results of extensive experiments run on synthetic and real datasets confirm our findings.

In this study, an irregular low‐density parity‐check (iLDPC) coded rate compatible modulation (iLDPC‐RCM) is proposed. A particularly designed interleaver is inserted between LDPC and RCM such that a fast convergence and a low bit‐error rate (BER) can be achieved. The combination of strong error correction capability of irregular LDPC code and the seamless adaptation of RCM enables the proposed scheme to achieve a robust and spectrally efficient transmission over time‐varying channels. In addition, a joint belief propagation algorithm is proposed to lower the BER of iLDPC‐RCM and speed up the convergence of iterative decoding. Simulation results show that the proposed iLDPC‐RCM improves the BER and throughput performance while maintaining an acceptable computational complexity at the same time, validating its advantages over the regular LDPC coded RCM with the same coding rate.

The 2-body correlation function (2-BCF) is a group of statistical measurements that found applications in many scientific domains. One type of 2-BCF named the Spatial Distance Histogram (SDH) is of vital importance in describing the physical features of natural systems. While a naïve way of computing SDH requires quadratic time, efficient algorithms based on resolving nodes in spatial trees have been developed. A key decision in the design of such algorithms is to choose a proper underlying data structure: our previous work utilizes quad-tree (oct-tree for 3-dimensional data) and in this paper we propose a kd-tree-based solution. Although it is easy to see that both implementations have the same time complexity O(N2d−1/d), where d is the number of dimensions of the dataset, a thorough comparison of their actual running time under different scenarios is conducted. In particular, we present an analytical model to rigorously quantify the running time of dual-tree algorithms. Our analysis suggests that the kd-tree-based implementation outperforms the quad-/oct-tree solution under all scenarios with different data sizes and query parameters. In particular, such performance advantage is shown as a speedup up to 1.23X over the quad-tree algorithm for 2D data. Results of extensive experiments run on synthetic and real datasets confirm our findings.

Particle simulation has become an important research tool in many scientific and engineering fields. Data generated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial distance histogram (SDH) query, is the building block of many high-level analytics, and requires quadratic time to compute using a straightforward algorithm. Previous work has developed efficient algorithms that compute exact SDHs. While beating the naive solution, such algorithms are still not practical in processing SDH queries against large-scale simulation data. In this paper, we take a different path to tackle this problem by focusing on approximate algorithms with provable error bounds. We first present a solution derived from the aforementioned exact SDH algorithm, and this solution has running time that is unrelated to the system size N. We also develop a mathematical model to analyze the mechanism that leads to errors in the basic approximate algorithm. Our model provides insights on how the algorithm can be improved to achieve higher accuracy and efficiency. Such insights give rise to a new approximate algorithm with improved time/accuracy tradeoff. Experimental results confirm our analysis.

In this paper, for an odd prime$p$and an integer$n \geq 3$, a new family of$p$-ary sequences of period${{p^{n}-1} \over {2}}$with low correlation is constructed. The new family is constructed by shifts and additions of two decimated sequences of a$p$-ary$m$-sequence, and its family size is$2(p^{n}-1)$. The complete correlation distribution of this new family is derived. It is also shown that the family is optimal with respect to the parameter$\theta_{{\rm rms}}$, which denotes the root mean square of all nontrivial correlations. Compared with the known sequence families, our sequence family is new and has a larger family size, which is four times of its period.

Particle simulation has become an important research tool in many scientific and engineering fields. Data generated by such simulations impose great challenges to database storage and query processing. One of the queries against particle simulation data, the spatial distance histogram (SDH) query, is the building block of many high-level analytics, and requires quadratic time to compute using a straightforward algorithm. In this paper, we propose a novel algorithm to compute SDH based on a data structure called density map, which can be easily implemented by augmenting a quad-tree index. We also show the results of rigorous mathematical analysis of the time complexity of the proposed algorithm: our algorithm runs on ominus(N3/2) for two-dimensional data and ominus(N5/3) for three-dimensional data, respectively. We also propose an approximate SDH processing algorithm whose running time is unrelated to the input size N. Experimental results confirm our analysis and show that the approximate SDH algorithm achieves very high accuracy.

In orthogonal frequency division multiplexing (OFDM) systems, rapid variations of doubly-selective fading channels lead to a loss of subcarrier orthogonality, resulting in inter-carrier interference (ICI) and system performance degradation. Although some methods have been proposed to suppress ICI, they are computationally complex or at the price of sacrificing spectral efficiency. In this paper, we provide an ICI analysis in both time- and frequency-domains while existing literatures analyze the ICI effects mainly in frequency domain. Based on this analysis, we propose a novel ICI mitigation scheme whose complexity is linear in the OFDM symbol length. The method uses iterative ICI cancellation in the time domain. We provide theoretical analysis and simulation results to show that the proposed method can effectively mitigate ICI caused by channel variations with a low computation complexity and high spectral efficiency.

In orthogonal frequency division multiplexing (OFDM) systems, when the length of the cyclic prefix (CP) is shorter than the channel length, the orthogonality between sub-channels is lost because of the intersymbol interference (ISI) and interchannel interference (ICI). In this case, the one-tap frequency domain equalizer can't be used any more. A time-domain equalizer (TEQ) is usually used in the receiver to reduce the duration of the overall response of the transmission system, and therefore minimize the ISI and ICI. However, the optimum design of TEQ turns out to be a very difficult task. In this paper, we propose a frequency domain equalizer (FEQ) for OFDM systems with insufficient CP, by making use of the presence of null side sub-carriers and the redundancy of CP. The equalizer has a sparse matrix structure and thus a low computational complexity. Theoretical analysis and simulation results show that it can efficiently remove ISI and ICI caused by insufficient CP and recover the transmitted data. Moreover, we derive the condition for the existence and uniqueness of FEQ, i.e., the combined length of CP and null sub-carriers is not shorter than the channel order. This means that the insufficiency of CP in time domain can be compensated by the redundancy of the null side sub-carriers in frequency domain.

A novel space-time coding scheme, called space-time cyclic-delay coding (STCDC), for multiple input multiple output orthogonal frequency-division multiplexing (MIMO-OFDM) systems over frequency-selective fading channels is introduced. The scheme exploits the redundancy introduced by channel coding. The transmitter antennas send the cyclically delayed copies of OFDM symbols, and the receiver uses the maximum likelihood estimation method to estimate the transmitted sequence. We show that STCDC-OFDM can achieve the maximum diversity, which is the product of the number of transmitter antennas (N/sub t/), the number of receiver antennas (N/sub r/) and the channel length (L), if the error control code has at least a free distance of N/sub t/L. Compared with the existing space-time coding and space-frequency coded MIMO-OFDM techniques, the proposed scheme has the advantages of being independent from the number of transmit antennas and having a lower implementation complexity.