arXiv subjects

Xiaohu Tang

Publications and source records attributed to Xiaohu Tang.

At least 73 records · Page 4Linked to original sources

arXiv2021

A Generic Transformation for Optimal Node Repair in MDS Array Codes over $\mathbf{F}_2$

For high-rate linear systematic maximum distance separable (MDS) codes, most early constructions could initially optimally repair all the systematic nodes but not all the parity nodes. Fortunately, this issue was first solved by Li et al. in (IEEE Trans. Inform. Theory, 64(9), 6257-6267, 2018), where a transformation that can convert any nonbinary MDS array code into another one with desired properties was proposed. However, the transformation does not work for binary MDS array codes. In this paper, we address this issue by proposing another generic transformation that can convert any $[n, k]$ binary MDS array code into a new one, which endows any $r=n-k\ge2$ chosen nodes with optimal repair bandwidth and optimal rebuilding access properties, and at the same time, preserves the normalized repair bandwidth/rebuilding access for the remaining $k$ nodes under some conditions. As two immediate applications, we show that 1) by applying the transformation multiple times, any binary MDS array code can be converted into one with optimal rebuilding access for all nodes, 2) any binary MDS array code with optimal repair bandwidth or optimal rebuilding access for the systematic nodes can be converted into one with the corresponding optimality property for all nodes.

cs.IT↗

arXiv2021

Symmetric Private Polynomial Computation From Lagrange Encoding

The problem of $X$-secure $T$-colluding symmetric Private Polynomial Computation (PPC) from coded storage system with $B$ Byzantine and $U$ unresponsive servers is studied in this paper. Specifically, a dataset consisting of $M$ files is stored across $N$ distributed servers according to $(N,K+X)$ Maximum Distance Separable (MDS) codes such that any group of up to $X$ colluding servers can not learn anything about the data files. A user wishes to privately evaluate one out of a set of candidate polynomial functions over the $M$ files from the system, while guaranteeing that any $T$ colluding servers can not learn anything about the identity of the desired function and the user can not learn anything about the $M$ data files more than the desired polynomial function evaluations, in the presence of $B$ Byzantine servers that can send arbitrary responses maliciously to confuse the user and $U$ unresponsive servers that will not respond any information at all. A novel symmetric PPC scheme using Lagrange encoding is proposed. This scheme achieves a PPC rate of $1-\frac{G(K+X-1)+T+2B}{N-U}$ with secrecy rate $\frac{G(K+X-1)+T}{N-(G(K+X-1)+T+2B+U)}$ and finite field size $N+\max\{K,N-(G(K+X-1)+T+2B+U)\}$, where $G$ is the maximum degree over all the candidate polynomial functions. Moreover, to further measure the efficiency of PPC schemes, upload cost, query complexity, server computation complexity and decoding complexity required to implement the scheme are analyzed. Remarkably, the PPC setup studied in this paper generalizes all the previous MDS coded PPC setups and the degraded schemes strictly outperform the best known schemes in terms of (asymptotical) PPC rate, which is the main concern of the PPC schemes.

cs.IT↗

arXiv2021

Multi-User Blind Symmetric Private Information Retrieval from Coded Servers

The problem of Multi-user Blind $X$-secure $T$-colluding Symmetric Private Information Retrieval from Maximum Distance Separable (MDS) coded storage system with $B$ Byzantine and $U$ unresponsive servers (U-B-MDS-MB-XTSPIR) is studied in this paper. Specifically, a database consisting of multiple files, each labeled by $M$ indices, is stored at the distributed system with $N$ servers according to $(N,K+X)$ MDS codes over $\mathbb{F}_q$ such that any group of up to $X$ colluding servers learn nothing about the data files. There are $M$ users, in which each user $m,m=1,\ldots,M$ privately selects an index $θ_m$ and wishes to jointly retrieve the file specified by the $M$ users' indices $(θ_1,\ldots,θ_M)$ from the storage system, while keeping its index $θ_m$ private from any $T_m$ colluding servers, where there exists $B$ Byzantine servers that can send arbitrary responses maliciously to confuse the users retrieving the desired file and $U$ unresponsive servers that will not respond any message at all. In addition, each user must not learn information about the other users' indices and the database more than the desired file. An U-B-MDS-MB-XTSPIR scheme is constructed based on Lagrange encoding. The scheme achieves a retrieval rate of $1-\frac{K+X+T_1+\ldots+T_M+2B-1}{N-U}$ with secrecy rate $\frac{K+X+T_1+\ldots+T_M-1}{ N-(K+X+T_1+\ldots+T_M+2B+U-1)}$ on the finite field of size $q\geq N+\max\{K, N-(K+X+T_1+\ldots+T_M+2B+U-1)\}$ for any number of files.

cs.IT↗

arXiv2021

Adaptive Gradient Coding

This paper focuses on mitigating the impact of stragglers in distributed learning system. Unlike the existing results designed for a fixed number of stragglers, we developed a new scheme called Adaptive Gradient Coding(AGC) with flexible tolerance of various number of stragglers. Our scheme gives an optimal tradeoff between computation load, straggler tolerance and communication cost. In particular, it allows to minimize the communication cost according to the real-time number of stragglers in the practical environments. Implementations on Amazon EC2 clusters using Python with mpi4py package verify the flexibility in several situations.

cs.IT↗

arXiv2021

A Construction of Maximally Recoverable Codes with Order-Optimal Field Size

We construct maximally recoverable codes (corresponding to partial MDS codes) which are based on linearized Reed-Solomon codes. The new codes have a smaller field size requirement compared with known constructions. For certain asymptotic regimes, the constructed codes have order-optimal alphabet size, asymptotically matching the known lower bound.

cs.IT↗

arXiv2021

Scalable Cell-Free Massive MIMO Systems with Finite Resolution ADCs/DACs over Spatially Correlated Rician Fading Channels

In this paper, an analytical framework for evaluating the performance of scalable cell-free massive MIMO (SCF-mMIMO) systems in which all user equipments (UEs) and access points (APs) employ finite resolution digital-to-analog converters (DACs) and analog-to-digital converters (ADCs) and operates under correlated Rician fading, is presented. By using maximal-ratio combining (MRC) detection, generic expressions for the uplink (UL) spectral efficiency (SE) for both distributed and centralized schemes are derived. In order to further reduce the computational complexity (CC) of the original local partial MMSE (LP-MMSE) and partial MMSE (P-MMSE) detectors, two novel scalable low complexity MMSE detectors are proposed for distributed and centralized schemes respectively, which achieves very similar SE performance. Furthermore, for the distributed scheme a novel partial large-scale fading decoding (P-LSFD) weighting vector is introduced and its analytical SE performance is very similar to the performance of an equivalent unscalable LSFD vector. Finally, a scalable algorithm jointly consisting of AP cluster formation, pilot assignment, and power control is proposed, which outperforms the conventional random pilot assignment and user-group based pilot assignment policies and, contrary to an equal power transmit strategy, it guarantees quality of service (QoS) fairness for all accessing UEs.

cs.IT↗

arXiv2021

A subfield-based construction of optimal linear codes over finite fields

In this paper, we construct four families of linear codes over finite fields from the complements of either the union of subfields or the union of cosets of a subfield, which can produce infinite families of optimal linear codes, including infinite families of (near) Griesmer codes. We also characterize the optimality of these four families of linear codes with an explicit computable criterion using the Griesmer bound and obtain many distance-optimal linear codes. In addition, we obtain several classes of distance-optimal linear codes with few weights and completely determine their weight distributions. It is shown that most of our linear codes are self-orthogonal or minimal which are useful in applications.

cs.IT↗

arXiv2021

An Accuracy-Lossless Perturbation Method for Defending Privacy Attacks in Federated Learning

Although federated learning improves privacy of training data by exchanging local gradients or parameters rather than raw data, the adversary still can leverage local gradients and parameters to obtain local training data by launching reconstruction and membership inference attacks. To defend such privacy attacks, many noises perturbation methods (like differential privacy or CountSketch matrix) have been widely designed. However, the strong defence ability and high learning accuracy of these schemes cannot be ensured at the same time, which will impede the wide application of FL in practice (especially for medical or financial institutions that require both high accuracy and strong privacy guarantee). To overcome this issue, in this paper, we propose \emph{an efficient model perturbation method for federated learning} to defend reconstruction and membership inference attacks launched by curious clients. On the one hand, similar to the differential privacy, our method also selects random numbers as perturbed noises added to the global model parameters, and thus it is very efficient and easy to be integrated in practice. Meanwhile, the random selected noises are positive real numbers and the corresponding value can be arbitrarily large, and thus the strong defence ability can be ensured. On the other hand, unlike differential privacy or other perturbation methods that cannot eliminate the added noises, our method allows the server to recover the true gradients by eliminating the added noises. Therefore, our method does not hinder learning accuracy at all.

cs.LG↗

arXiv2021

Several classes of bent functions over finite fields

Let $\mathbb{F}_{p^{n}}$ be the finite field with $p^n$ elements and $\operatorname{Tr}(\cdot)$ be the trace function from $\mathbb{F}_{p^{n}}$ to $\mathbb{F}_{p}$, where $p$ is a prime and $n$ is an integer. Inspired by the works of Mesnager (IEEE Trans. Inf. Theory 60(7): 4397-4407, 2014) and Tang et al. (IEEE Trans. Inf. Theory 63(10): 6149-6157, 2017), we study a class of bent functions of the form $f(x)=g(x)+F(\operatorname{Tr}(u_1x),\operatorname{Tr}(u_2x),\cdots,\operatorname{Tr}(u_τx))$, where $g(x)$ is a function from $\mathbb{F}_{p^{n}}$ to $\mathbb{F}_{p}$, $τ\geq2$ is an integer, $F(x_1,\cdots,x_n)$ is a reduced polynomial in $\mathbb{F}_{p}[x_1,\cdots,x_n]$ and $u_i\in \mathbb{F}^{*}_{p^n}$ for $1\leq i \leq τ$. As a consequence, we obtain a generic result on the Walsh transform of $f(x)$ and characterize the bentness of $f(x)$ when $g(x)$ is bent for $p=2$ and $p>2$ respectively. Our results generalize some earlier works. In addition, we study the construction of bent functions $f(x)$ when $g(x)$ is not bent for the first time and present a class of bent functions from non-bent Gold functions.

cs.IT↗

arXiv2021

A Generic Transformation to Generate MDS Storage Codes with $δ$-Optimal Access Property

For high-rate maximum distance separable (MDS) codes, most of them are designed to optimally repair a single failed node by connecting all the surviving nodes. However, in practical systems, sometimes not all the surviving nodes are available. To facilitate the practical storage system, a few constructions of $(n,k)$ MDS codes with the property that any single failed node can be optimally repaired by accessing any $d$ surviving nodes have been proposed, where $d\in [k+1:n-1)$. However, all of them either have large sub-packetization levels or are not explicit for all the parameters. To address these issues, we propose a generic transformation that can convert any $(n',k')$ MDS code to another $(n,k)$ MDS code with the optimal repair property and optimal access property for an arbitrary set of two nodes, while the repair efficiency of the remaining $n-2$ nodes can be kept. By recursively applying the generic transformation to a scalar MDS code multiple times, we get an MDS code with the optimal repair property and the optimal access property for all nodes, which outperforms previous known MDS codes in terms of either the sub-packetization level or the flexibility of the parameters.

cs.IT↗

arXiv2021

Improved Constructions for Secure Multi-Party Batch Matrix Multiplication

This paper investigates the problem of Secure Multi-party Batch Matrix Multiplication (SMBMM), where a user aims to compute the pairwise products $\mathbf{A}\divideontimes\mathbf{B}\triangleq(\mathbf{A}^{(1)}\mathbf{B}^{(1)},\ldots,\mathbf{A}^{(M)}\mathbf{B}^{(M)})$ of two batch of massive matrices $\mathbf{A}$ and $\mathbf{B}$ that are generated from two sources, through $N$ honest but curious servers which share some common randomness. The matrices $\mathbf{A}$ (resp. $\mathbf{B}$) must be kept secure from any subset of up to $X_{\mathbf{A}}$ (resp. $X_\mathbf{B}$) servers even if they collude, and the user must not obtain any information about $(\mathbf{A},\mathbf{B})$ beyond the products $\mathbf{A}\divideontimes\mathbf{B}$. A novel computation strategy for single secure matrix multiplication problem (i.e., the case $M=1$) is first proposed, and then is generalized to the strategy for SMBMM by means of cross subspace alignment. The SMBMM strategy focuses on the tradeoff between recovery threshold (the number of successful computing servers that the user needs to wait for), system cost (upload cost, the amount of common randomness, and download cost) and system complexity (encoding, computing, and decoding complexities). Notably, compared with the known result by Chen et al., the strategy for the degraded case $X= X_{\mathbf{A}}=X_{\mathbf{B}}$ achieves better recovery threshold, amount of common randomness, download cost and decoding complexity when $X$ is less than some parameter threshold, while the performance with respect to other measures remain identical.

cs.IT↗

arXiv2021

A class of APcN power functions over finite fields of even characteristic

In this paper, we investigate the power functions $F(x)=x^d$ over the finite field $\mathbb{F}_{2^{4n}}$, where $n$ is a positive integer and $d=2^{3n}+2^{2n}+2^{n}-1$. It is proved that $F(x)=x^d$ is APcN at certain $c$'s in $\mathbb{F}_{2^{4n}}$, and it is the second class of APcN power functions over finite fields of even characteristic. Further, the $c$-differential spectrum of these power functions is also determined.

cs.IT↗

arXiv2021

Achieve Efficient Position-Heap-based Privacy-Preserving Substring-of-Keyword Query over Cloud

The cloud computing technique, which was initially used to mitigate the explosive growth of data, has been required to take both data privacy and users' query functionality into consideration. Symmetric searchable encryption (SSE) is a popular solution to supporting efficient keyword queries over encrypted data in the cloud. However, most of the existing SSE schemes focus on the exact keyword query and cannot work well when the user only remembers the substring of a keyword, i.e., substring-of-keyword query. This paper aims to investigate this issue by proposing an efficient and privacy-preserving substring-of-keyword query scheme over cloud. First, we employ the position heap technique to design a novel tree-based index to match substrings with corresponding keywords. Based on the tree-based index, we introduce our substring-of-keyword query scheme, which contains two consecutive phases. The first phase queries the keywords that match a given substring, and the second phase queries the files that match a keyword in which people are really interested. In addition, detailed security analysis and experimental results demonstrate the security and efficiency of our proposed scheme.

cs.CR↗

arXiv2021

Capacity-Achieving Private Information Retrieval Schemes from Uncoded Storage Constrained Servers with Low Sub-packetization

This paper investigates reducing sub-packetization of capacity-achieving schemes for uncoded Storage Constrained Private Information Retrieval (SC-PIR) systems. In the SC-PIR system, a user aims to retrieve one out of $K$ files from $N$ servers while revealing nothing about its identity to any individual server, in which the $K$ files are stored at the $N$ servers in an uncoded form and each server can store up to $μK$ equivalent files, where $μ$ is the normalized storage capacity of each server. We first prove that there exists a capacity-achieving SC-PIR scheme for a given storage design if and only if all the packets are stored exactly at $M\triangleq μN$ servers for $μ$ such that $M=μN\in\{2,3,\ldots,N\}$. Then, the optimal sub-packetization for capacity-achieving linear SC-PIR schemes is characterized as the solution to an optimization problem, which is typically hard to solve because of involving indicator functions. Moreover, a new notion of array called Storage Design Array (SDA) is introduced for the SC-PIR system. With any given SDA, an associated capacity-achieving SC-PIR scheme is constructed. Next, the SC-PIR schemes that have equal-size packets are investigated. Furthermore, the optimal equal-size sub-packetization among all capacity-achieving linear SC-PIR schemes characterized by Woolsey et al. is proved to be $\frac{N(M-1)}{\gcd(N,M)}$. Finally, by allowing unequal size of packets, a greedy SDA construction is proposed, where the sub-packetization of the associated SC-PIR scheme is upper bounded by $\frac{N(M-1)}{\gcd(N,M)}$. Among all capacity-achieving linear SC-PIR schemes, the sub-packetization is optimal when $\min\{M,N-M\}|N$ or $M=N$, and within a multiplicative gap $\frac{\min\{M,N-M\}}{\gcd(N,M)}$ of the optimal one otherwise. In particular, for the case $N=d\cdot M\pm1$ where $d\geq 2$, another SDA is constructed to obtain lower sub-packetization.

cs.IT↗

arXiv2020

On the differential spectrum of a class of power functions over finite fields

Differential uniformity is a significant concept in cryptography as it quantifies the degree of security of S-boxes respect to differential attacks. Power functions of the form $F(x)=x^d$ with low differential uniformity have been extensively studied in the past decades due to their strong resistance to differential attacks and low implementation cost in hardware. In this paper, we give an affirmative answer to a recent conjecture proposed by Budaghyan, Calderini, Carlet, Davidova and Kaleyski about the differential uniformity of $F(x)=x^d$ over $\mathbb{F}_{2^{4n}}$, where $n$ is a positive integer and $d=2^{3n}+2^{2n}+2^{n}-1$, and we completely determine its differential spectrum.

cs.IT↗

arXiv2020

A Systematic Construction of MDS Codes With Small Sub-packetization Level and Near-Optimal Repair Bandwidth

In the literature, all the known high-rate MDS codes with the optimal repair bandwidth possess a significantly large sub-packetization level, which may prevent the codes to be implemented in practical systems. To build MDS codes with small sub-packetization level, existing constructions and theoretical bounds imply that one may sacrifice the optimality of the repair bandwidth. Partly motivated by the work of Tamo et al. (IEEE Trans. Inform. Theory, 59(3), 1597-1616, 2013), in this paper, we present a transformation that can greatly reduce the sub-packetization level of MDS codes with the optimal repair bandwidth with respect to the same code length n. As applications of the transformation, four high-rate MDS codes having both small sub-packetization level and near-optimal repair bandwidth can be obtained, where three of them are explicit and the required field sizes are around or even smaller than the code length n. Additionally, we propose another explicit MDS code which has a similar structure as that of the first resultant code obtained by the generic transformation, but can be built on a smaller finite field.

cs.IT↗

arXiv2020

Optimal Locally Repairable Codes: An Improved Bound and Constructions

We study the Singleton-type bound that provides an upper limit on the minimum distance of locally repairable codes. We present an improved bound by carefully analyzing the combinatorial structure of the repair sets. Thus, we show the previous bound is unachievable for certain parameters. We then also provide explicit constructions of optimal codes that show that for certain parameters the new bound is sharp. Additionally, as a byproduct, some previously known codes are shown to attain the new bound and are thus proved to be optimal.

cs.IT↗

arXiv2020

Dual-comb delay spectroscopy with attometer resolution

Spectroscopy has attracted much attention in molecular detection, biomolecular identification, and chemical analysis for providing accurate measurement. However, it is almost unable to distinguish different sources with overlapped resonances in mixed analytes. Here, we present dual-comb delay spectroscopy to overcome this problem. The introduction of group delay spectroscopy provides a new tool to identify sources that would lead to overlapped resonances in intensity or phase spectroscopy. To obtain sufficiently high spectral resolution and signal-to-noise ratio for achieving reliable group delay spectrum, a probe comb with the wavelengths precisely scaned by a microwave source is applied, leading to attometer-level resolution and million-level signal-to-noise ratio. In an experiment, spectroscopy with an optional resolution up to 1 kHz (8 attometer), an average signal-to-noise ratio surpassing 2,000,000, and a span exceeding 33 nm is demonstrated. Two overlapped resonances from two different sources are clearly differentiated. Our work offers a new perspective for exploring the interaction between matter and light.

physics.ins-det↗