Convolutional Codes of Goppa Type

A new kind of Convolutional Codes generalizing Goppa Codes is proposed. This provides a systematic method for constructing convolutional codes with prefixed properties. In particular, examples of Maximum-Distance Separable (MDS) convolutional codes are obtained.This research was partially supported by the Spanish DGI through research project BFM2003-00078 and by the Junta de Castilla y León through research projects SA071/04 and SA032/02.     

On the dimension of Goppa codes

A lower bound for the dimension of geometric BCH codes (i.e. subfield subcodes of Goppa codes) has been given by M. Wirtz [7]. We prove that this bound is actually exact for small enough divisorG.     

Turbo codes with symmetric and asymmetric component codes defined over finite fields of integers

Binary asymmetric turbo codes and non-binary turbo codes have been proposed to improve the bit error rate (BER) performance of parallel concatenated coding schemes. Both strategies have certain advantages that can be exploited when they are put together. This paper investigates turbo codes based on two component recursive systematic convolutional (RSC) codes defined over a finite field of integers. Symmetric and asymmetric non-binary turbo codes are obtained and their BER performance in both the `waterfall? and the `error-floor? regions is analysed. The results show good performance improvements when compared to binary and quaternary turbo codes with same throughput.     

Extended Classical Goppa Codes

We construct extended classical Goppa codes that can have unrestricted block length. The parameters of the codes are estimated, and the standard Berlekamp–Massey error processor is adapted to the codes. Received: July 5, 1999; revised version: February 25, 2000     

Effective homotopy of fibrations

The well-known effective homology method provides algorithms computing homology groups of spaces. The main idea consists in keeping systematically a deep and subtle connection between the homology of any object and the object itself. Now applying similar ideas to the computation of homotopy groups, we aim to develop a new effective homotopy theory which allows one to determine homotopy groups of spaces. In this work we introduce the notion of a solution for the homotopical problem of a simplicial set, which will be the main definition of our theory, and present an algorithm computing the effective homotopy of a fibration. We also illustrate with examples some applications of our results.     

On Doubly-Cyclic Convolutional Codes

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra , where is a finite field. A particular choice of the data leads to the class of doubly-cyclic CC’s. Within this large class Reed-Solomon and BCH convolutional codes can be defined. After constructing doubly-cyclic CC’s, basic properties are derived on the basis of which distance properties of Reed-Solomon convolutional codes are investigated. This shows that some of them are optimal or near optimal with respect to distance and performance.     

Heterogeneous Hyperedge Convolutional Network

Graph convolutional networks (GCNs) have been developed as a general andpowerful tool to handle various tasks related to graph data. However, current methodsmainly consider homogeneous networks and ignore the rich semantics and multiple typesof objects that are common in heterogeneous information networks (HINs). In this paper,we present a Heterogeneous Hyperedge Convolutional Network (HHCN), a novel graphconvolutional network architecture that operates on HINs. Specifically, we extract therich semantics by different metastructures and adopt hyperedge to model the interactionsamong metastructure-based neighbors. Due to the powerful information extractioncapabilities of metastructure and hyperedge, HHCN has the flexibility to model thecomplex relationships in HINs by setting different combinations of metastructures andhyperedges. Moreover, a metastructure attention layer is also designed to allow each nodeto select the metastructures based on their importance and provide potentialinterpretability for graph analysis. As a result, HHCN can encode node features,metastructure-based semantics and hyperedge information simultaneously by aggregatingfeatures from metastructure-based neighbors in a hierarchical manner. We evaluateHHCN by applying it to the semi-supervised node classification task. Experimentalresults show that HHCN outperforms state-of-the-art graph embedding models andrecently proposed graph convolutional network models.     

Construction of Improved Geometric Goppa Codes from Klein Curves and Klein-like Curves

Linear error-correcting codes, especially Reed-Solomon codes, find applications in communication and computer memory systems, to enhance their reliability and data integrity. In this paper, we present Improved Geometric Goppa (IGG) codes, a new class of error-correcting codes, based on the principles of algebraic-geometry. We also give a reasonably low complexity procedure for the construction of these IGG codes from Klein curves and Klein-like curves, in plane and high-dimensional spaces. These codes have good code parameters like minimum distance rate and information rate, and have the potential to replace the conventional Reed-Solomon codes in most practical applications. Based on the approach discussed in this paper, it might be possible to construct a class of codes whose performance exceeds the Gilbert-Varshamov bound. Received: November 14, 1995; revised version: November 22, 1999     

Sentiment Classification Based on Piecewise Pooling Convolutional Neural Network

Recently, the effectiveness of neural networks, especially convolutional neural networks, has been validated in the field of natural language processing, in which, sentiment classification for online reviews is an important and challenging task. Existing convolutional neural networks extract important features of sentences without local features or the feature sequence. Thus, these models do not perform well, especially for transition sentences. To this end, we propose a Piecewise Pooling Convolutional Neural Network (PPCNN) for sentiment classification. Firstly, with a sentence presented by word vectors, convolution operation is introduced to obtain the convolution feature map vectors. Secondly, these vectors are segmented according to the positions of transition words in sentences. Thirdly, the most significant feature of each local segment is extracted using max pooling mechanism, and then the different aspects of features can be extracted. Specifically, the relative sequence of these features is preserved. Finally, after processed by the dropout algorithm, the softmax classifier is trained for sentiment classification. Experimental results show that the proposed method PPCNN is effective and superior to other baseline methods, especially for datasets with transition sentences.     

基于浅层卷积神经网络的面部表情识别

面部表情识别在人机交互等领域中发挥着重要作用,采用深度学习方法提高了模型精度,但过深的网络加大了计算成本,造成识别滞后和性能低下的问题.本文提出了一种浅层卷积神经网络模型,它受到Xception网络的启发,结合了残差模块和深度可分离卷积,同时引入了功能模块与网络进行融合.微调后的网络结构简单、模型较小,在FER2013...     

Convolutional Codes and Coherent Sheaves

We present a sheaf-theoretic setting for convolutional codes in that coherent sheaves (over a projective line) play the same role as finite-dimensional linear spaces in the theory of block codes. Using coherent sheaves (and their cohomologies), we give natural straightforward proofs of the main results on the structural properties of convolutional codes. Received: May 7, 1999; revised version: August 11, 2000     

Nanodisk codes

We report a new encoding system based upon dispersible arrays of nanodisks prepared by on-wire lithography and functionalized with Raman active chromophores. These nanodisk arrays are encoded both physically (in a "barcode" pattern) and spectroscopically (Raman) along the array. These structures can be used in covert encoding strategies because of their small size or as biological labels with readout by scanning confocal Raman spectroscopy. As proof-of-concept, we demonstrate their utility in DNA detection in a multiplexed format at target concentrations as low as 100 fM.     

Maximum Distance Separable Convolutional Codes

A maximum distance separable (MDS) block code is a linear code whose distance is maximal among all linear block codes of rate k/n. It is well known that MDS block codes do exist if the field size is more than n. In this paper we generalize this concept to the class of convolutional codes of a fixed rate k/n and a fixed code degree δ. In order to achieve this result we will introduce a natural upper bound for the free distance generalizing the Singleton bound. The main result of the paper shows that this upper bound can be achieved in all cases if one allows sufficiently many field elements. Received: December 10, 1998; revised version: May 14, 1999     

基于Spinal码的编码协作

针对5G的高速率传输需求,研究了基于Spinal码的编码协作。基于Spinal码的无速率性,提出了直接选用不同通道内所有编码符号实现编码协作的CC-SPSC方案。在此方案基础上,考虑基站在设备条件和中心调度方面的优势,引入以基站为控制核心的策略,提出了CC-SPSC-BSC-AL方案和CC-SPSC-BSC-SR方案。仿真结果表明,所提方案在模拟信道和数字信道下均有显著的误码率性能提升,尤其是CC-SPSC和CC-SPSC-BSCSR方案,分别在模拟信道和数字信道下的应用优势突出。     

基于稀疏子空间的卷积神经网络目标跟踪

针对粒子滤波目标跟踪过程中初始化和权值退化的数据处理情况,在粒子滤波框架下提出一种基于稀疏子空间的卷积神经网络目标跟踪算法。以仿生学为基础,在目标跟踪过程中引入稀疏子空间和卷积神经网络。首先,利用稀疏子空间模型筛选出与目标状态相似度较高的候选区域进行后续跟踪处理,减少冗余计算并降低跟踪的复杂性;然后,将稀疏子空间输出用作卷积神经网络的输入,并利用卷积神经网络模型对图像数据处理的优点进行目标跟踪的数据处理;最后,通过对目标数据的不断更新来减少目标表观变化的影响。实验表明,该算法能够更好地处理目标跟踪中的目标遮挡、运动模糊、光流与尺度变化,提高算法的准确性和数据处理能力。     

基于卷积神经网络的印刷套准识别方法

目的 针对目前印刷套准识别方法依赖于经验人工设计特征提取的问题,提出一种不需要人工提取图像特征的卷积神经网络模型,实现印刷套准状态的识别.方法 采用图像增强技术实现不均衡训练集的均衡化,增加训练集图像的数量,提高模型的识别准确率.设计基于AlexNet网络结构的印刷套准识别模型的结构参数,分析批处理样本数量和基础学习率对模型性能的影响规律.结果 文中方法获得的总印刷套准识别准确率为0.9860,召回率为1.0000,分类准确率几何平均数为0.9869.结论 文中方法能自动提取图像特征,不依赖于人工设计的特征提取方法.在构造的数据集上,文中方法的分类性能优于实验中的支持向量机方法.     

Function-field codes

Function-field codes provide a general perspective on the construction of algebraic-geometry codes. We briefly review the theory of function-field codes and establish some new results in this theory, including a propagation rule. We show how to derive linear codes from function-field codes, thus generalizing a construction of linear codes due to Xing, Niederreiter, and Lam. The research of the second and third author was partially supported by the DSTA research grant R-394-000-025-422 with Temasek Laboratories in Singapore.     

Skew-cyclic codes

We generalize the notion of cyclic codes by using generator polynomials in (non commutative) skew polynomial rings. Since skew polynomial rings are left and right euclidean, the obtained codes share most properties of cyclic codes. Since there are much more skew-cyclic codes, this new class of codes allows to systematically search for codes with good properties. We give many examples of codes which improve the previously best known linear codes.     

基于跨层卷积神经网络的石刻碑文识别

石刻碑文的研究具有重要的历史价值和文化价值,但是由于受到自然环境的风化、腐蚀和人为的破坏,碑刻文字存在很大的识别难度.传统的识别方法通过选择特征的提取方式,得到笔画、部首等浅层特征,准确率不高.卷积神经网络可以利用深层网络自动提取到更抽象的特征用于识别,具有更高的准确率.本文针对碑刻数据收集困难,数据量较少的问题,提出了一种基于VGG-16的跨层卷积神经网络进行石刻碑文的识别,使用投影分割改进法实现碑文的分割,该方法在本文构建的测试数据集上对石刻碑文的识别具有很好的效果.     

Construction and decoding of matrix-product codes from nested codes

We consider matrix-product codes ${[C_1\cdots C_s] \cdot A}$ , where ${C_1, \ldots , C_s}$ are nested linear codes and matrix A has full rank. We compute their minimum distance and provide a decoding algorithm when A is a non-singular by columns matrix. The decoding algorithm decodes up to half of the minimum distance.