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Zhixiong Chen

Publications and source records attributed to Zhixiong Chen.

At least 37 records · Page 2Linked to original sources

Knowledge-aided Federated Learning for Energy-limited Wireless Networks

The conventional model aggregation-based federated learning (FL) approach requires all local models to have the same architecture, which fails to support practical scenarios with heterogeneous local models. Moreover, frequent model exchange is costly for resource-limited wireless networks since modern deep neural networks usually have over a million parameters. To tackle these challenges, we propose a novel knowledge-aided FL (KFL) framework, which aggregates light high-level data features, namely knowledge, in the per-round learning process. This framework allows devices to design their machine-learning models independently and reduces the communication overhead in the training process. We then theoretically analyze the convergence bound of the proposed framework, revealing that scheduling more data volume in each round helps to improve the learning performance. In addition, large data volume should be scheduled in early rounds if the total scheduled data volume during the entire learning course is fixed. Inspired by this, we define a new objective function, i.e., the weighted scheduled data sample volume, to transform the inexplicit global loss minimization problem into a tractable one for device scheduling, bandwidth allocation, and power control. To deal with unknown time-varying wireless channels, we transform the considered problem into a deterministic problem for each round with the assistance of the Lyapunov optimization framework. Then, we derive the optimal bandwidth allocation and power control solution and develop an efficient online device scheduling algorithm to achieve an energy-learning trade-off in the learning process. Experimental results on MNIST and CIFAR-10 show that the proposed KFL is capable of reducing over 99% communication overhead while achieving better learning performance than the conventional model aggregation-based algorithms.

eess.SP↗

Privacy-Preserving Electricity Theft Detection based on Blockchain

In most electricity theft detection schemes, consumers' power consumption data is directly input into the detection center. Although it is valid in detecting the theft of consumers, the privacy of all consumers is at risk unless the detection center is assumed to be trusted. In fact, it is impractical. Moreover, existing schemes may result in some security problems, such as the collusion attack due to the presence of a trusted third party, and malicious data tampering caused by the system operator (SO) being attacked. Aiming at the problems above, we propose a blockchain-based privacy-preserving electricity theft detection scheme without a third party. Specifically, the proposed scheme uses an improved functional encryption scheme to enable electricity theft detection and load monitoring while preserving consumers' privacy; distributed storage of consumers' data with blockchain to resolve security problems such as data tampering, etc. Meanwhile, we build a long short-term memory network (LSTM) model to perform higher accuracy for electricity theft detection. The proposed scheme is evaluated in a real environment, and the results show that it is more accurate in electricity theft detection within acceptable communication and computational overhead. Our system analysis demonstrates that the proposed scheme can resist various security attacks and preserve consumers' privacy.

cs.CR↗

Efficient Wireless Federated Learning with Partial Model Aggregation

The data heterogeneity across devices and the limited communication resources, e.g., bandwidth and energy, are two of the main bottlenecks for wireless federated learning (FL). To tackle these challenges, we first devise a novel FL framework with partial model aggregation (PMA). This approach aggregates the lower layers of neural networks, responsible for feature extraction, at the parameter server while keeping the upper layers, responsible for complex pattern recognition, at devices for personalization. The proposed PMA-FL is able to address the data heterogeneity and reduce the transmitted information in wireless channels. Then, we derive a convergence bound of the framework under a non-convex loss function setting to reveal the role of unbalanced data size in the learning performance. On this basis, we maximize the scheduled data size to minimize the global loss function through jointly optimize the device scheduling, bandwidth allocation, computation and communication time division policies with the assistance of Lyapunov optimization. Our analysis reveals that the optimal time division is achieved when the communication and computation parts of PMA-FL have the same power. We also develop a bisection method to solve the optimal bandwidth allocation policy and use the set expansion algorithm to address the device scheduling policy. Compared with the benchmark schemes, the proposed PMA-FL improves 3.13\% and 11.8\% accuracy on two typical datasets with heterogeneous data distribution settings, i.e., MINIST and CIFAR-10, respectively. In addition, the proposed joint dynamic device scheduling and resource management approach achieve slightly higher accuracy than the considered benchmarks, but they provide a satisfactory energy and time reduction: 29\% energy or 20\% time reduction on the MNIST; and 25\% energy or 12.5\% time reduction on the CIFAR-10.

cs.LG↗

Dynamic Task Software Caching-assisted Computation Offloading for Multi-Access Edge Computing

In multi-access edge computing (MEC), most existing task software caching works focus on statically caching data at the network edge, which may hardly preserve high reusability due to the time-varying user requests in practice. To this end, this work considers dynamic task software caching at the MEC server to assist users' task execution. Specifically, we formulate a joint task software caching update (TSCU) and computation offloading (COMO) problem to minimize users' energy consumption while guaranteeing delay constraints, where the limited cache size and computation capability of the MEC server, as well as the time-varying task demand of users are investigated. This problem is proved to be non-deterministic polynomial-time hard, so we transform it into two sub-problems according to their temporal correlations, i.e., the real-time COMO problem and the Markov decision process-based TSCU problem. We first model the COMO problem as a multi-user game and propose a decentralized algorithm to address its Nash equilibrium solution. We then propose a double deep Q-network (DDQN)-based method to solve the TSCU policy. To reduce the computation complexity and convergence time, we provide a new design for the deep neural network (DNN) in DDQN, named state coding and action aggregation (SCAA). In SCAA-DNN, we introduce a dropout mechanism in the input layer to code users' activity states. Additionally, at the output layer, we devise a two-layer architecture to dynamically aggregate caching actions, which is able to solve the huge state-action space problem. Simulation results show that the proposed solution outperforms existing schemes, saving over 12% energy, and converges with fewer training episodes.

eess.SP↗

Arithmetic Autocorrelation of Binary $m$-Sequences

An $m$-sequence is the one of the largest period among those produced by a linear feedback shift register. It possesses several desirable features of pseudorandomness such as balance, uniform pattern distribution and ideal autocorrelation for applications to communications. However, it also possesses undesirable features such as low linear complexity. Here we prove a nontrivial upper bound on its arithmetic autocorrelation, another figure of merit introduced by Mandelbaum for error-correcting codes and later investigated by Goresky and Klapper for FCSRs. The upper bound is close to half of the period and hence rather large, which gives an undesirable feature.

cs.IT↗

Arithmetic crosscorrelation of pseudorandom binary sequences of coprime periods

The (classical) crosscorrelation is an important measure of pseudorandomness of two binary sequences for applications in communications. The arithmetic crosscorrelation is another figure of merit introduced by Goresky and Klapper generalizing Mandelbaum's arithmetic autocorrelation. First we observe that the arithmetic crosscorrelation is constant for two binary sequences of coprime periods which complements the analogous result for the classical crosscorrelation. Then we prove upper bounds for the constant arithmetic crosscorrelation of two Legendre sequences of different periods and of two binary $m$-sequences of coprime periods, respectively.

cs.CR↗

Correlation measures of binary sequences derived from Euler quotients

Fermat-Euler quotients arose from the study of the first case of Fermat's Last Theorem, and have numerous applications in number theory. Recently they were studied from the cryptographic aspects by constructing many pseudorandom binary sequences, whose linear complexities and trace representations were calculated. In this work, we further study their correlation measures by using the approach based on Dirichlet characters, Ramanujan sums and Gauss sums. Our results show that the $4$-order correlation measures of these sequences are very large. Therefore they may not be suggested for cryptography.

math.NT↗

Correlation, Linear Complexity, Maximum order Complexity on Families of binary Sequences

Correlation measure of order $k$ is an important measure of randomness in binary sequences. This measure tries to look for dependence between several shifted version of a sequence. We study the relation between the correlation measure of order $k$ and another two pseudorandom measures: the $N$th linear complexity and the $N$th maximum order complexity. We simplify and improve several state-of-the-art lower bounds for these two measures using the Hamming bound as well as weaker bounds derived from it.

cs.IT↗

On the 4-adic complexity of the two-prime quaternary generator

R. Hofer and A. Winterhof proved that the 2-adic complexity of the two-prime (binary) generator of period $pq$ with two odd primes $p\neq q$ is close to its period and it can attain the maximum in many cases. When the two-prime generator is applied to producing quaternary sequences, we need to determine the 4-adic complexity. We present the formulae of possible values of the 4-adic complexity, which is larger than $pq-\log_4(pq^2)-1$ if $p<q$. So it is good enough to resist the attack of the rational approximation algorithm.

cs.CR↗

Math Course Redesign in a Private Four Year Hispanic Serving Institute to Address Diverse Equitable and Inclusive Issues

We identified three most challenging points related to diverse, equitable, and inclusive (DEI) issues. First, the majority of our students entering the College lack the math skills essential to success in Calculus, as basic as College Algebra, some others have a multi-year gap after graduating high school. Almost all but a few STEM students must start from College Algebra before they can move on to Precalculus and then Calculus. Secondly, we noted that many students who planned to pursue STEM dropped out of their majors because they couldn't obtain the required grade in College Algebra to move forward. This is one of the main reasons that the enrollment of calculus classes is consistently low. Lastly, a large portion of basic math classes are taught by adjunct instructors, the turnover ratio among adjunct instructors is not small. One such consequence is that many students don't have equitable learning experiences and some students are still struggling with College Algebra even in the calculus class. In this paper, we describe an illustrative case study of a college-wide initiative to tackle the DEI issues.

math.HO↗

On $q$-nearly bent Boolean functions

For each non-constant Boolean function $q$, Klapper introduced the notion of $q$-transforms of Boolean functions. The {\em $q$-transform} of a Boolean function $f$ is related to the Hamming distances from $f$ to the functions obtainable from $q$ by nonsingular linear change of basis. In this work we discuss the existence of $q$-nearly bent functions, a new family of Boolean functions characterized by the $q$-transform. Let $q$ be a non-affine Boolean function. We prove that any balanced Boolean functions (linear or non-linear) are $q$-nearly bent if $q$ has weight one, which gives a positive answer to an open question (whether there exist non-affine $q$-nearly bent functions) proposed by Klapper. We also prove a necessary condition for checking when a function isn't $q$-nearly bent.

math.CO↗

On the $k$-error linear complexity of binary sequences derived from the discrete logarithm in finite fields

Let $q=p^r$ be a power of an odd prime $p$. We study binary sequences $σ=(σ_0,σ_1,\ldots)$ with entries in $\{0,1\}$ defined by using the quadratic character $χ$ of the finite field $\mathbb{F}_q$: $$ σ_n=\left\{ \begin{array}{ll} 0,& \mathrm{if}\quad n= 0,\\ (1-χ(ξ_n))/2,&\mathrm{if}\quad 1\leq n< q, \end{array} \right. $$ for the ordered elements $ξ_0,ξ_1,\ldots,ξ_{q-1}\in \mathbb{F}_q$. The $σ$ is Legendre sequence if $r=1$. Our first contribution is to prove a lower bound on the linear complexity of $σ$ for $r\geq 2$. The bound improves some results of Meidl and Winterhof. Our second contribution is to study the $k$-error linear complexity of $σ$ for $r=2$. It seems that we cannot settle the case when $r>2$ and leave it open.

cs.CR↗

The 2-adic complexity of a class of binary sequences with optimal autocorrelation magnitude

Recently, a class of binary sequences with optimal autocorrelation magnitude has been presented by Su et al. based on interleaving technique and Ding-Helleseth-Lam sequences (Des. Codes Cryptogr., https://doi.org/10.1007/s10623-017-0398-5). And its linear complexity has been proved to be large enough to resist the B-M Algorighm (BMA) by Fan (Des. Codes Cryptogr., https://doi.org/10.1007/s10623-018-0456-7). In this paper, we study the 2-adic complexity of this class of binary sequences. Our result shows that the 2-adic complexity of this class of sequence is no less than one half of its period, i.e., its 2-adic complexity is large enough to resist the Rational Aproximation Algorithm (RAA).

cs.IT↗

On error linear complexity of new generalized cyclotomic binary sequences of period $p^2$

We consider the $k$-error linear complexity of a new binary sequence of period $p^2$, proposed in the recent paper "New generalized cyclotomic binary sequences of period $p^2$", by Z. Xiao et al., who calculated the linear complexity of the sequences (Designs, Codes and Cryptography, 2017, https://doi.org/10.1007/s10623-017-0408-7). More exactly, we determine the values of $k$-error linear complexity over $\mathbb{F}_2$ for almost $k>0$ in terms of the theory of Fermat quotients. Results indicate that such sequences have good stability.

cs.CR↗

On $k$-error linear complexity of pseudorandom binary sequences derived from Euler quotients

We investigate the $k$-error linear complexity of pseudorandom binary sequences of period $p^{\mathfrak{r}}$ derived from the Euler quotients modulo $p^{\mathfrak{r}-1}$, a power of an odd prime $p$ for $\mathfrak{r}\geq 2$. When $\mathfrak{r}=2$, this is just the case of polynomial quotients (including Fermat quotients) modulo $p$, which has been studied in an earlier work of Chen, Niu and Wu. In this work, we establish a recursive relation on the $k$-error linear complexity of the sequences for the case of $\mathfrak{r}\geq 3$. We also state the exact values of the $k$-error linear complexity for the case of $\mathfrak{r}=3$. From the results, we can find that the $k$-error linear complexity of the sequences (of period $p^{\mathfrak{r}}$) does not decrease dramatically for $k<p^{\mathfrak{r}-2}(p-1)^2/2$.

cs.CR↗

On the $q$-Bentness of Boolean Functions

For each non-constant $q$ in the set of $n$-variable Boolean functions, the {\em $q$-transform} of a Boolean function $f$ is related to the Hamming distances from $f$ to the functions obtainable from $q$ by nonsingular linear change of basis. Klapper conjectured that no Boolean function exists with its $q$-transform coefficients equal to $\pm 2^{n/2}$ (such function is called $q$-bent). In our early work, we only gave partial results to confirm this conjecture for small $n$. Here we prove thoroughly that the conjecture is true by investigating the nonexistence of the partial difference sets in Abelian groups with special parameters. We also introduce a new family of functions called almost $q$-bent functions, which are close to $q$-bentness.

cs.CR↗

Linear complexity of Legendre-polynomial quotients

We continue to investigate binary sequence $(f_u)$ over $\{0,1\}$ defined by $(-1)^{f_u}=\left(\frac{(u^w-u^{wp})/p}{p}\right)$ for integers $u\ge 0$, where $\left(\frac{\cdot}{p}\right)$ is the Legendre symbol and we restrict $\left(\frac{0}{p}\right)=1$. In an earlier work, the linear complexity of $(f_u)$ was determined for $w=p-1$ under the assumption of $2^{p-1}\not\equiv 1 \pmod {p^2}$. In this work, we give possible values on the linear complexity of $(f_u)$ for all $1\le w<p-1$ under the same conditions. We also state that the case of larger $w(\geq p)$ can be reduced to that of $0\leq w\leq p-1$.

cs.CR↗

Linear complexity of quaternary sequences over Z_4 derived from generalized cyclotomic classes modulo 2p

We determine the exact values of the linear complexity of 2p-periodic quaternary sequences over Z_4 (the residue class ring modulo 4) defined from the generalized cyclotomic classes modulo 2p in terms of the theory of of Galois rings of characteristic 4, where p is an odd prime. Compared to the case of quaternary sequences over the finite field of order 4, it is more dificult and complicated to consider the roots of polynomials in Z_4[X] due to the zero divisors in Z_4 and hence brings some interesting twists. We answer an open problem proposed by Kim, Hong and Song.

math.NT↗