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Xiaohu Tang

Publications and source records attributed to Xiaohu Tang.

107 records · Page 6Linked to original sources
arXiv2017

The Optimal Placement Delivery Arrays

In wireless networks, coded caching is an effective technique to reduce network congestion during peak traffic times. Recently, a new concept called placement delivery array (PDA) was proposed to characterize the coded caching scheme. So far, only one class of PDAs by Maddah-Ali and Niesen is known to be optimal. In this paper, we mainly focus on constructing optimal PDAs. Firstly, we derive some lower bounds. Next, we present several infinite classes of PDAs, which are shown to be optimal with respect to the new bounds.

cs.IT↗
arXiv2016

On the Placement Delivery Array Design in Centralized Coded Caching Scheme

Caching is a promising solution to satisfy the ever increasing demands for the multi-media traffics. In caching networks, coded caching is a recently proposed technique that achieves significant performance gains over the uncoded caching schemes. However, to implement the coded caching schemes, each file has to be split into $F$ packets, which usually increases exponentially with the number of users $K$. Thus, designing caching schemes that decrease the order of $F$ is meaningful for practical implementations. In this paper, by reviewing the Ali-Niesen caching scheme, the placement delivery array (PDA) design problem is firstly formulated to characterize the placement issue and the delivery issue with a single array. Moreover, we show that, through designing appropriate PDA, new centralized coded caching schemes can be discovered. Secondly, it is shown that the Ali-Niesen scheme corresponds to a special class of PDA, which realizes the best coding gain with the least $F$. Thirdly, we present a new construction of PDA for the centralized caching system, wherein the cache size of each user $M$ (identical cache size is assumed at all users) and the number of files $N$ satisfies $M/N=1/q$ or ${(q-1)}/{q}$ ($q$ is an integer such that $q\geq 2$). The new construction can decrease the required $F$ from the order $O\left(e^{K\cdot\left(\frac{M}{N}\ln \frac{N}{M} +(1-\frac{M}{N})\ln \frac{N}{N-M}\right)}\right)$ of Ali-Niesen scheme to $O\left(e^{K\cdot\frac{M}{N}\ln \frac{N}{M}}\right)$ or $O\left(e^{K\cdot(1-\frac{M}{N})\ln\frac{N}{N-M}}\right)$ respectively, while the coding gain loss is only $1$.

cs.IT↗
arXiv2016

A Novel Sufficient Condition for Generalized Orthogonal Matching Pursuit

Generalized orthogonal matching pursuit (gOMP), also called orthogonal multi-matching pursuit, is an extension of OMP in the sense that $N\geq1$ indices are identified per iteration. In this paper, we show that if the restricted isometry constant (RIC) $δ_{NK+1}$ of a sensing matrix $\A$ satisfies $δ_{NK+1} < 1/\sqrt {K/N+1}$, then under a condition on the signal-to-noise ratio, gOMP identifies at least one index in the support of any $K$-sparse signal $\x$ from $\y=\A\x+\v$ at each iteration, where $\v$ is a noise vector. Surprisingly, this condition does not require $N\leq K$ which is needed in Wang, \textit{et al} 2012 and Liu, \textit{et al} 2012. Thus, $N$ can have more choices. When $N=1$, it reduces to be a sufficient condition for OMP, which is less restrictive than that proposed in Wang 2015. Moreover, in the noise-free case, it is a sufficient condition for accurately recovering $\x$ in $K$ iterations which is less restrictive than the best known one. In particular, it reduces to the sharp condition proposed in Mo 2015 when $N=1$.

cs.IT↗
arXiv2016

On the Coded Caching Delivery Design over Wireless Networks

Coded caching scheme is a promising technique to migrate the network burden in peak hours, which attains more prominent gains than the uncoded caching. The coded caching scheme can be classified into two types, namely, the centralized and the decentralized scheme, according to whether the placement procedures are carefully designed or operated at random. However, most of the previous analysis assumes that the connected links between server and users are error-free. In this paper, we explore the coded caching based delivery design in wireless networks, where all the connected wireless links are different. For both centralized and decentralized cases, we proposed two delivery schemes, namely, the orthogonal delivery scheme and the concurrent delivery scheme. We focus on the transmission time slots spent on satisfying the system requests, and prove that for both the centralized and the decentralized cases, the concurrent delivery always outperforms orthogonal delivery scheme. Furthermore, for the orthogonal delivery scheme, we derive the gap in terms of transmission time between the decentralized and centralized case, which is essentially no more than 1.5.

cs.IT↗
arXiv2016

Placement Delivery Array Design through Strong Edge Coloring of Bipartite Graphs

The technique of coded caching proposed by Madddah-Ali and Niesen is a promising approach to alleviate the load of networks during busy times. Recently, placement delivery array (PDA) was presented to characterize both the placement and delivery phase in a single array for the centralized coded caching algorithm. In this paper, we interpret PDA from a new perspective, i.e., the strong edge coloring of bipartite graph. We prove that, a PDA is equivalent to a strong edge colored bipartite graph. Thus, we can construct a class of PDAs from existing structures in bipartite graphs. The class includes the scheme proposed by Maddah-Ali \textit{et al.} and a more general class of PDAs proposed by Shangguan \textit{et al.} as special cases. Moreover, it is capable of generating a lot of PDAs with flexible tradeoff between the sub-packet level and load.

cs.IT↗
arXiv2016

Optimal Locally Repairable Systematic Codes Based on Packings

Locally repairable codes are desirable for distributed storage systems to improve the repair efficiency. In this paper, we first build a bridge between locally repairable code and packing. As an application of this bridge, some optimal locally repairable codes can be obtained by packings, which gives optimal locally repairable codes with flexible parameters.

cs.IT↗
arXiv2016

A Novel Compressive Sensing based Enhanced Multiplexing Scheme for MIMO System

A novel compressive-sensing based signal multiplexing scheme is proposed in this paper to further improve the multiplexing gain for multiple input multiple output (MIMO) system. At the transmitter side, a Gaussian random measurement matrix in compressive sensing is employed before the traditional spatial multiplexing in order to carry more data streams on the available spatial multiplexing streams of the underlying MIMO system. At the receiver side, it is proposed to reformulate the detection of the multiplexing signal into two steps. In the first step, the traditional MIMO equalization can be used to restore the transmitted spatial multiplexing signal of the MIMO system. While in the second step, the standard optimization based detection algorithm assumed in the compressive sensing framework is utilized to restore the CS multiplexing data streams, wherein the exhaustive over-complete dictionary is used to guarantee the sparse representation of the CS multiplexing signal. In order to avoid the excessive complexity, the sub-block based dictionary and the sub-block based CS restoration is proposed. Finally, simulation results are presented to show the feasibility of the proposed CS based enhanced MIMO multiplexing scheme. And our efforts in this paper shed some lights on the great potential in further improving the spatial multiplexing gain for the MIMO system.

cs.IT↗
arXiv2015

Bounds and Constructions for $\overline{3}$-Separable Codes with Length $3$

Separable codes were introduced to provide protection against illegal redistribution of copyrighted multimedia material. Let $\mathcal{C}$ be a code of length $n$ over an alphabet of $q$ letters. The descendant code ${\sf desc}(\mathcal{C}_0)$ of $\mathcal{C}_0 = \{{\bf c}_1, {\bf c}_2, \ldots, {\bf c}_t\} \subseteq {\mathcal{C}}$ is defined to be the set of words ${\bf x} = (x_1, x_2, \ldots,x_n)^T$ such that $x_i \in \{c_{1,i}, c_{2,i}, \ldots, c_{t,i}\}$ for all $i=1, \ldots, n$, where ${\bf c}_j=(c_{j,1},c_{j,2},\ldots,c_{j,n})^T$. $\mathcal{C}$ is a $\overline{t}$-separable code if for any two distinct $\mathcal{C}_1, \mathcal{C}_2 \subseteq \mathcal{C}$ with $|\mathcal{C}_1| \le t$, $|\mathcal{C}_2| \le t$, we always have ${\sf desc}(\mathcal{C}_1) \neq {\sf desc}(\mathcal{C}_2)$. Let $M(\overline{t},n,q)$ denote the maximal possible size of such a separable code. In this paper, an upper bound on $M(\overline{3},3,q)$ is derived by considering an optimization problem related to a partial Latin square, and then two constructions for $\overline{3}$-SC$(3,M,q)$s are provided by means of perfect hash families and Steiner triple systems.

cs.IT↗
arXiv2015

On the Systematic Constructions of Rotation Symmetric Bent Functions with Any Possible Algebraic Degrees

In the literature, few constructions of $n$-variable rotation symmetric bent functions have been presented, which either have restriction on $n$ or have algebraic degree no more than $4$. In this paper, for any even integer $n=2m\ge2$, a first systemic construction of $n$-variable rotation symmetric bent functions, with any possible algebraic degrees ranging from $2$ to $m$, is proposed.

cs.IT↗
arXiv2015

A Framework of Constructions of Minimal Storage Regenerating Codes with the Optimal Access/Update Property

In this paper, we present a generic framework for constructing systematic minimum storage regenerating codes with two parity nodes based on the invariant subspace technique. Codes constructed in our framework not only contain some best known codes as special cases, but also include some new codes with key properties such as the optimal access property and the optimal update property. In particular, for a given storage capacity of an individual node, one of the new codes has the largest number of systematic nodes and two of the new codes have the largest number of systematic nodes with the optimal update property.

cs.IT↗
arXiv2014

A Sytematic Piggybacking Design for Minimum Storage Regenerating Codes

Piggybacking is an efficient method to decrease the repair bandwidth of Maximum Distance Separable (MDS) codes or Minimum Storage Regenerating (MSR) codes. In this paper, for minimizing the repair bandwidth of parity nodes of the known MSR codes with high rate, which is usually the whole size of the original data, i.e., the maximal, a new systematic piggybacking design is proposed through an in-depth analysis of the design of piggybacking. As a result, new MSR codes are obtained with almost optimal repair bandwidth of parity nodes while retaining the optimal repair bandwidth of systematic nodes. Furthermore, MSR codes with balanced download during node repair process are presented based on the new piggybacking design.

cs.IT↗
arXiv2013

Optimal Ternary Cyclic Codes with Minimum Distance Four and Five

Cyclic codes are an important subclass of linear codes and have wide applications in data storage systems, communication systems and consumer electronics. In this paper, two families of optimal ternary cyclic codes are presented. The first family of cyclic codes has parameters $[3^m-1, 3^m-1-2m, 4]$ and contains a class of conjectured cyclic codes and several new classes of optimal cyclic codes. The second family of cyclic codes has parameters $[3^m-1, 3^m-2-2m, 5]$ and contains a number of classes of cyclic codes that are obtained from perfect nonlinear functions over $\fthreem$, where $m>1$ and is a positive integer.

cs.IT↗
arXiv2012

Characterization of Negabent Functions and Construction of Bent-Negabent Functions with Maximum Algebraic Degree

We present necessary and sufficient conditions for a Boolean function to be a negabent function for both even and odd number of variables, which demonstrate the relationship between negabent functions and bent functions. By using these necessary and sufficient conditions for Boolean functions to be negabent, we obtain that the nega spectrum of a negabent function has at most 4 values. We determine the nega spectrum distribution of negabent functions. Further, we provide a method to construct bent-negabent functions in $n$ variables ($n$ even) of algebraic degree ranging from 2 to $\frac{n}{2}$, which implies that the maximum algebraic degree of an $n$-variable bent-negabent function is equal to $\frac{n}{2}$. Thus, we answer two open problems proposed by Parker and Pott and by Stǎnicǎ \textit{et al.} respectively.

cs.IT↗
arXiv2012

A Note on a Conjecture for Balanced Elementary Symmetric Boolean Functions

In 2008, Cusick {\it et al.} conjectured that certain elementary symmetric Boolean functions of the form $σ_{2^{t+1}l-1, 2^t}$ are the only nonlinear balanced ones, where $t$, $l$ are any positive integers, and $σ_{n,d}=\bigoplus_{1\le i_1<...<i_d\le n}x_{i_1}x_{i_2}...x_{i_d}$ for positive integers $n$, $1\le d\le n$. In this note, by analyzing the weight of $σ_{n, 2^t}$ and $σ_{n, d}$, we prove that ${\rm wt}(σ_{n, d})<2^{n-1}$ holds in most cases, and so does the conjecture. According to the remainder of modulo 4, we also consider the weight of $σ_{n, d}$ from two aspects: $n\equiv 3({\rm mod\}4)$ and $n\not\equiv 3({\rm mod\}4)$. Thus, we can simplify the conjecture. In particular, our results cover the most known results. In order to fully solve the conjecture, we also consider the weight of $σ_{n, 2^t+2^s}$ and give some experiment results on it.

cs.IT↗
arXiv2010

Construction of Frequency Hopping Sequence Set Based upon Generalized Cyclotomy

Frequency hopping (FH) sequences play a key role in frequency hopping spread spectrum communication systems. It is important to find FH sequences which have simultaneously good Hamming correlation, large family size and large period. In this paper, a new set of FH sequences with large period is proposed, and the Hamming correlation distribution of the new set is investigated. The construction of new FH sequences is based upon Whiteman's generalized cyclotomy. It is shown that the proposed FH sequence set is optimal with respect to the average Hamming correlation bound.

cs.IT↗