On Some Properties of Graph of Prefix Code

We investigate decomposition of codes and finite languages. A prime decomposition is a decomposition of a code or languages into a concatenation of nontrivial prime codes or languages. A code is prime if it cannot be decomposed into at least two nontrivial codes as the same for the languages. In the paper, a linear time algorithm is designed, which finds the prime decomposition. If codes or finite languages are presented as given by its minimal deterministic automaton, then from the point of view of abstract algebra and graph theory, this automaton has special properties. The study was conducted using system for computational Discrete Algebra GAP. .

Jointly-check iterative decoding algorithm for quantum sparse graph codes

For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms standard BP algorithm with an obvious performance improvement.

Totally Coded Method for Signal Flow Graph Algorithm

After a code-table has been established by means of node association information from signal flow graph, the totally coded method (TCM) is applied merely in the domain of code operation beyond any figure-earching algorithm. The code-series (CS) have the holo-information nature, so that both the content and the sign of each gain-term can be determined via the coded method. The principle of this method is simple and it is suited for computer programming. The capability of the computer-aided analysis for switched current network (SIN) can be enhanced.

Self-dual Codes Defined on Factor Graphs

A definition of a self-dual code on graph and a procedure based on factor graphs to judge a self-dual code were presented. Three contributions of this paper were described as follows. To begin with, transform T_ R→L were defined, which was the basis of self-dual codes defined on graphs and played a key role in the paper. The second were that a self-dual code could be defined on factor graph, which was much different from conventional algebraic method. The third was that a factor graph approach to judge a self-dual code was illustrated, which took advantage of duality properties of factor graphs and our proposed transform T_ R→L to offer a convenient and geometrically intuitive process to judge a self-dual code.

Two-level Bregmanized method for image interpolation with graph regularized sparse coding

A two-level Bregmanized method with graph regularized sparse coding （TBGSC） is presented for image interpolation. The outer-level Bregman iterative procedure enforces the observation data constraints, while the inner-level Bregmanized method devotes to dictionary updating and sparse represention of small overlapping image patches. The introduced constraint of graph regularized sparse coding can capture local image features effectively, and consequently enables accurate reconstruction from highly undersampled partial data. Furthermore, modified sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge within a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can effectively reconstruct images and it outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.

Construction of Short-Block Nonbinary LDPC Codes Based on Cyclic Codes

In this paper, we focus on shortblock nonbinary LDPC(NB-LDPC) codes based on cyclic codes. Based on Tanner graphs' isomorphism, we present an efficient search algorithm for finding non-isomorphic binary cyclic LDPC codes. Notice that the parity-check matrix H of the resulting code is square and not of full rank, and its row weight and column weight are the same. By replacing the ones in the same column of H with a nonzero element of fi nite fi elds GF(q), a class of NB-LDPC codes over GF(q) is obtained. Numerical results show that the constructed codes perform well over the AWGN channel and have fast decoding convergence. Therefore, the proposed NB-LDPC codes provide a promising coding scheme for low-latency and high-reliability communications.

Graph Regularized Sparse Coding Method for Highly Undersampled MRI Reconstruction

The imaging speed is a bottleneck for magnetic resonance imaging( MRI) since it appears. To alleviate this difficulty,a novel graph regularized sparse coding method for highly undersampled MRI reconstruction( GSCMRI) was proposed. The graph regularized sparse coding showed the potential in maintaining the geometrical information of the data. In this study, it was incorporated with two-level Bregman iterative procedure that updated the data term in outer-level and learned dictionary in innerlevel. Moreover,the graph regularized sparse coding and simple dictionary updating stages derived by the inner minimization made the proposed algorithm converge in few iterations, meanwhile achieving superior reconstruction performance. Extensive experimental results have demonstrated GSCMRI can consistently recover both real-valued MR images and complex-valued MR data efficiently,and outperform the current state-of-the-art approaches in terms of higher PSNR and lower HFEN values.

<i>L</i>(0, 1)-Labelling of Cactus Graphs

An L(0,1)-labelling of a graph G is an assignment of nonnegative integers to the vertices of G such that the difference between the labels assigned to any two adjacent vertices is at least zero and the difference between the labels assigned to any two vertices which are at distance two is at least one. The span of an L(0,1)-labelling is the maximum label number assigned to any vertex of G. The L(0,1)-labelling number of a graph G, denoted by λ0.1(G) is the least integer k such that G has an L(0,1)-labelling of span k. This labelling has an application to a computer code assignment problem. The task is to assign integer control codes to a network of computer stations with distance restrictions. A cactus graph is a connected graph in which every block is either an edge or a cycle. In this paper, we label the vertices of a cactus graph by L(0,1)-labelling and have shown that, △-1≤λ0.1(G)≤△ for a cactus graph, where △ is the degree of the graph G.

JOINT ITERATIVE DECODING FOR SIMPLE-ENCODING SYSTEMATIC IRREGULAR-LDPC-BASED CODED COOPERATION IN NON-IDEAL RELAY CHANNEL

In this paper, a new kind of simple-encoding irregular systematic LDPC codes suitable for one-relay coded cooperation is designed, where the proposed joint iterative decoding is effectively performed in the destination which is in accordance with the corresponding joint Tanner graph characterizing two different component LDPC codes used by the source and relay in ideal and non-ideal relay cooperations. The theoretical analysis and simulations show that the coded cooperation scheme obviously outperforms the coded non-cooperation one under the same code rate and decoding complex. The significant performance improvement can be virtually credited to the additional mutual exchange of the extrinsic information resulted by the LDPC code employed by the source and its counterpart used by the relay in both ideal and non-ideal cooperations.

Two-Level Bregman Method for MRI Reconstruction with Graph Regularized Sparse Coding

In this paper, a two-level Bregman method is presented with graph regularized sparse coding for highly undersampled magnetic resonance image reconstruction. The graph regularized sparse coding is incorporated with the two-level Bregman iterative procedure which enforces the sampled data constraints in the outer level and updates dictionary and sparse representation in the inner level. Graph regularized sparse coding and simple dictionary updating applied in the inner minimization make the proposed algorithm converge with a relatively small number of iterations. Experimental results demonstrate that the proposed algorithm can consistently reconstruct both simulated MR images and real MR data efficiently, and outperforms the current state-of-the-art approaches in terms of visual comparisons and quantitative measures.

On the Girth of Tanner (5,7) Quasi-Cyclic LDPC Codes

The girth plays an important role in the design of LDPC codes. In order to determine the girth of Tanner(5,7) quasi-cyclic( QC) LDPC codes with length 7p for p being a prime with the form 35 m + 1,the cycles of lengths 4,6,8,and 10 are analyzed. Then these cycles are classified into sixteen categories,each of which can be expressed as an ordered block sequence,or a certain type. It is also shown that the existence of these cycles is equal to polynomial equations over Fpwho has a 35th unit root. We check if these polynomial equations have a 35th unit root and obtain the girth values of Tanner(5,7) QC LDPC codes.

On Locating Numbers of Graphs

Let G =( V,E) be a connected graph and W = { w_1,w_2,…,w_k} be an ordered subset of V( G).For any vertex v ∈V,the locating code of v with respect to W is the k-vector CW( v) = { d( v,w_1),d( v,w_2),…,d( v,w_k) },W is said to be a locating set of G if distinct vertices have the distinct locating code,and the locating number of G is defined as: Loc( G) = min{ | W| : W is a locating set of G}.We study the locating set and locating number of a graph G,obtain some bounds for the locating numbers of graphs,and determine the exact value of Loc( G) for some special classes of graphs,such as cycles,wheels,complete t-partite graph and some Cartesian products of paths and cycles. In addition,we also prove that Loc( T) ≥Δ-1 holds for all trees T with maximum degree Δ,and shows a tree T with Loc( T) = Δ-1.

Application of Rollout Strategy to Test Points Selection for Integer-Coded Fault Wise Table

Test points selection for integer-coded fault wise table is a discrete optimization problem. The global minimum set of test points can only be guaranteed by an exhaustive search which is eompurationally expensive. In this paper, this problem is formulated as a heuristic depth-first graph search problem at first. The graph node expanding method and rules are given. Then, rollout strategies are applied, which can be combined with the heuristic graph search algorithms, in a computationally more efficient manner than the optimal strategies, to obtain solutions superior to those using the greedy heuristic algorithms. The proposed rollout-based test points selection algorithm is illustrated and tested using an analog circuit and a set of simulated integer-coded fault wise tables. Computa- tional results are shown, which suggest that the rollout strategy policies are significantly better than other strategies.

Joint Iterative Decoding for Network-Coding-Based Multisource LDPC-Coded Cooperative MIMO

A network-coding-based multisource LDPC-coded cooperative MIMO scheme is proposed,where multiple sources transmit their messages to the destination with the assistance from a single relay.The relay cooperates with multiple sources simultaneously via network-coding.It avoids the issues of imperfect frequency/timing synchronization and large transmission delay which may be introduced by frequency-division multiple access(FDMA)/code-division multiple access(CDMA)and time-division multiple access(TDMA)manners.The proposed joint″Min-Sum″iterative decoding is effectively carried out in the destination.Such a decoding algorithm agrees with the introduced equivalent joint Tanner graph which can be used to fully characterize LDPC codes employed by the sources and relay.Theoretical analysis and numerical simulation show that the proposed scheme with joint iterative decoding can achieve significant cooperation diversity gain.Furthermore,for the relay,compared with the cascade scheme,the proposed scheme has much lower complexity of LDPC-encoding and is easier to be implemented in the hardware with similar bit error rate(BER)performance.

基于EBRCG的API结构模式信息增强方法研究

针对API调用模式缺乏结构信息及结果高冗余等问题,提出了基于扩展的分支保留调用图(the Extended Branch-Reserving Call Graph,EBRCG)的API结构模式信息增强方法。以Java开源项目源代码为研究对象,使用EBRCG来表示Java类的方法的结构信息,在EBRCG中,同时考虑了API调用语句、分支语句(将if语句和所有循环语句视为分支语句)、switch-case多分支语句、异常语句等,并提出了EBRCG裁剪算法来获取特定API调用模式的代码结构。同时,采用聚类和排序的方法对API调用模式的多个代码结构信息进行筛选,最终选择具有代表性的API调用模式的代码结构。为验证该方法的效果,将该方法与TextRank方法进行了3组实验比较。结果显示,该方法能有效地获取API调用模式的代码结构,相比TextRank方法能更准确地描述API的使用,有一定的研究意义,并为软件开发人员提供了参考。

面向代码搜索的函数功能多重图嵌入

如何提高异构的自然语言查询输入和高度结构化程序语言源代码的匹配准确度,是代码搜索的一个基本问题.代码特征的准确提取是提高匹配准确度的关键之一.代码语句表达的语义不仅与其本身有关,还与其所处的上下文相关.代码的结构模型为理解代码功能提供了丰富的上下文信息.提出一个基于函数功能多重图嵌入的代码搜索方法.在所提方法中,使用早期融合的策略,将代码语句的数据依赖关系融合到控制流图中,构建函数功能多重图来表示代码.该多重图通过数据依赖关系显式表达控制流图中缺乏的非直接前驱后继节点的依赖关系,增强语句节点的上下文信息.同时,针对多重图的边的异质性,采用关系图卷积网络方法从函数多重图中提取代码的特征.在公开数据集的实验表明,相比现有基于代码文本和结构模型的方法,所提方法的MRR提高5%以上.通过消融实验也表明控制流图较数据依赖图在搜索准确度上贡献较大.

基于多维关联规则的车辆故障码解耦方法研究

本文提出一种针对车辆复杂耦合故障的故障码(DTC)解耦方法。首先由车辆故障自诊断原理及故障信号传播过程分析故障码的复杂关联性,结合关联规则技术挖掘故障码间强关联关系,并定义故障码多维关联规则;其次由故障码数据集特征,改进适用于故障码多维关联规则挖掘的FP-Growth算法;最后由多维关联规则构建故障码关联知识图谱,结合图论实现复杂故障码解耦。结果表明,该方法能有效降低故障码的数量及复杂度,提升基于故障码检修故障的效率。

知识图谱特征重构下无线传感网络数据存储恢复

为了提升无线传感网络数据存储恢复成功率,保障无线传感网络数据存储安全性,提出知识图谱特征重构下无线传感网络数据存储恢复方法。通过基于知识图谱的特征重构方法优化数据存储结构;利用BP神经网络和LEACH算法,对特征重构后的数据进行融合。最后,结合多级网络编码和纠删码的原理,构建多级编码矩阵对融合数据进行多级编码,并生成多份数据副本进行存储,实现无线传感网络数据存储恢复。实验结果表明,该方法能够提升数据存储恢复成功率至90%以上,通信代价低于1.5×10^(5) Mbit/s,存储恢复时间低于0.7 ms,可以在提升恢复成功率的同时,降低存储通信代价和存储恢复时间。

嵌入式处理器自定义指令迭代识别方法仿真

嵌入式系统中的硬件资源是有限的,并且自定义指令和原始指令之间可能存在冲突,导致指令代码识别精准度降低、运行功耗较高。为此,提出嵌入式处理器自定义指令迭代低功耗识别方法。对嵌入式处理器的指令代码展开可视化处理,将指令图像输入卷积神经网络中,检测指令代码中存在的恶意代码,采用开源编译器将代码转变为控制数据流图,枚举并选择子图,通过代码转换完成嵌入式处理器自定义指令识别。仿真结果表明,所提方法的恶意代码检测精度高、代码识别准确率高,始终保持在70%以上,平均能耗仅为89J。

模板运算代码的自动生成与调优框架

针对现有模板代码生成方法不支持多图形处理器(GPU)、调优不充分等问题,提出一种由领域专用语言(DSL)描述的模板代码的自动生成与调优框架。在代码自动生成阶段,该框架能够自动解析上层提供的描述语言,构建计算图进而生成模板运算的统一计算设备架构(CUDA)核函数,同时根据单GPU或多GPU环境生成不同的主机端代码。在代码调优阶段,根据不同的GPU型号确定候选参数范围,动态调用生成的CUDA核函数以确定最优参数。在多GPU的情况下,自动生成的主机端代码能够使用计算与通信重叠的方法进行边界数据交换。在4种不同的GPU与7、13、19、27点模板运算中,该框架能找到最优的参数配置。实验结果表明,对于Tesla V100-SXM2,以调优过的参数进行模板运算,该框架在单精度4种模板运算下的每秒万亿次浮点运算数(TFLOPs)分别为1.230、1.680、1.120、1.480,在双精度下分别为0.690、1.010、0.480、1.470,平均性能达到手工优化代码的98%,并且描述更简单,支持多GPU扩展。