Coding Problem Research Articles

Guaranteeing Information Transfer Integrity Through Two Non-Colluding Malicious Nodes Against i.i.d. Attacks

This paper considers channel coding problems with the requirement of guaranteeing information integrity in the presence of malicious relays (MRs). The proved random channel coding scheme yields to an achievable rate formula which is identical to its counterpart obtained in the non-MRs system as long as a non-manipulable condition is satisfied. No pre-shared secret or secret transmission is needed for the proved scheme. Hence the obtained rate is generally larger than those achieved based on secret transmission schemes. In addition, we further prove that the systems with binary symmetric channels (BSCs) and binary erasure channels (BECs) are readily to satisfy the non-manipulable condition. Simulations based on turbo codes are also presented. The results indicate that our theoretical work is still available to practical channel codes.

New Constructions of Subspace Codes Using Subsets of MRD Codes in Several Blocks

A basic problem for the constant dimension subspace coding is to determine the maximal possible size A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> (n, d, k) of a set of k-dimensional subspaces in F <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sup> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> such that the subspace distance satisfies d(U, V ) = 2k - 2 dim (U ∩ V ) ≥ d for any two different subspaces U and V in this set. We present two new constructions of constant dimension subspace codes using subsets of maximum rank-distance (MRD) codes in several blocks. This method is firstly applied to the linkage construction and secondly to arbitrary number of blocks of lifting MRD codes. In these two constructions, subsets of MRD codes with bounded ranks play an essential role. The Delsarte theorem about the rank distribution of MRD codes is an important ingredient to count codewords in our constructed constant dimension subspace codes. We give many new lower bounds for A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">q</sub> (n, d, k). More than 110 new constant dimension subspace codes better than previously best known codes are constructed.

Semantic Predictive Coding with Arbitrated Generative Adversarial Networks

In spatio-temporal predictive coding problems, like next-frame prediction in video, determining the content of plausible future frames is primarily based on the image dynamics of previous frames. We establish an alternative approach based on their underlying semantic information when considering data that do not necessarily incorporate a temporal aspect, but instead they comply with some form of associative ordering. In this work, we introduce the notion of semantic predictive coding by proposing a novel generative adversarial modeling framework which incorporates the arbiter classifier as a new component. While the generator is primarily tasked with the anticipation of possible next frames, the arbiter’s principal role is the assessment of their credibility. Taking into account that the denotative meaning of each forthcoming element can be encapsulated in a generic label descriptive of its content, a classification loss is introduced along with the adversarial loss. As supported by our experimental findings in a next-digit and a next-letter scenario, the utilization of the arbiter not only results in an enhanced GAN performance, but it also broadens the network’s creative capabilities in terms of the diversity of the generated symbols.

Conference matrices from Legendre C-pairs

Introduction: There are just a few known methods for the construction of symmetric C-matrices, due to the lack of a universal structure for them. This obstruction is fundamental, in addition, the structure of C-matrices with a double border is incompletely described in literature, which makes its study especially relevant. The purpose: To describe the two-border two-circulant construction in detail with the proposal of the concept of C-pairs Legendre. Results: The paper deals with C-matrices of order n=2v+2 with two borders and extends the so called generalized Legendre pairs, v odd, to a wider class of Legendre C-pairs with even and odd v, defined on a finite abelian group G of order v. Such a pair consists of two functions a, b: G→Z, whose values are +1 or −1 except that a(e)=0, where e is the identity element of G and Z is the ring of integers. To characterize the Legendre C-pairs we use the subsets X={xÎG: a(x)=–1} and Y={xÎG: b(x)=–1} of G. We show that a(x−1)=(−1)v a(x) for all x. For odd v we show that X and Y form a difference family, which is not true for even v. These difference families are precisely the so called Szekeres difference sets, used originally for the construction of skew-Hadamard matrices. We introduce the subclass of the special Legendre C-pairs and prove that they exist whenever 2v+1 is a prime power. In the last two sections of the paper we list examples of special cyclic Legendre C-pairs for lengths v&lt;70. Practical relevance: C-matrices are used extensively in the problems of error-free coding, compression and masking of video information. Programs for search of conference matrices and a library of constructed matrices are used in the mathematical network “mathscinet.ru” together with executable on-line algorithms.

Совместимость и несовместимость коммуникативных систем английского и русского языков в области пожарно-технической коммуникации

To exchange information in some joint activities the communication is necessary which can be both verbal and non-verbal. The authors compare possible links between Russian and English elements of in the field of fire safety communication which will help to receive, process and transmit information from one subject to another both in Russian and English. The problem of understanding cultural codes performing certain functions in a particular language communication system (Russian and English) is discussed. The principles of communication systems combinability of Russian and English languages enables interaction are considered. The article presents the basic functions of the word as a unit of foreign language professional communication. Special attention is paid to monologue and dialogue speech which is important for mutual understanding. Clichéd speech patterns used in professional speech of fire-fighting services in Russia and Great Britain are presented. It is described non-verbal means of communication play an important role in transmitting certain information in the professional activity of fire safety specialists on the example of two countries.

Optimal Coding and the Origins of Zipfian Laws

ABSTRACT The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding – under an arbitrary coding scheme – and show that it predicts Zipf’s law of abbreviation, namely a tendency in natural languages for more frequent words to be shorter. We apply this result to investigate optimal coding also under so-called non-singular coding, a scheme where unique segmentation is not warranted but codes stand for a distinct number. Optimal non-singular coding predicts that the length of a word should grow approximately as the logarithm of its frequency rank, which is again consistent with Zipf’s law of abbreviation. Optimal non-singular coding in combination with the maximum entropy principle also predicts Zipf’s rank-frequency distribution. Furthermore, our findings on optimal non-singular coding challenge common beliefs about random typing. It turns out that random typing is in fact an optimal coding process, in stark contrast with the common assumption that it is detached from cost cutting considerations. Finally, we discuss the implications of optimal coding for the construction of a compact theory of Zipfian laws more generally as well as other linguistic laws.

Decoding Binary Linear Codes Over Channels With Synchronization Errors

Time synchronization is crucial for the safe and reliable operation of the fifth generation (5G) network, especially for applications requiring ultra-reliable low-latency data transmissions. The time synchronization problem, however, becomes increasingly challenging in high-mobility scenarios because the channel conditions, e.g., the multipath delay spread may vary rapidly. While there exist numerous works on the design of efficient channel decoding algorithms, decoding linear codes such as polar codes in the presence of synchronization errors is a less-explored topic. In this paper, we aim to fill this void and develop a systemic approach to decode general binary linear codes over binary symmetric channels with synchronization errors in which the lack of synchronization is modeled as the deletion channel model. The maximum likelihood (ML) decoding problem for binary linear codes over deletion channels is first formulated as a nonlinear optimization problem, in which a set of linear constraints are employed to characterize the input-output relationship of a deletion channel. It turns out that both the objective function and the constraints of this optimization problem are nonlinear, which poses significant challenges against the design of efficient decoding algorithms. As a remedy, we first replace the nonlinear objective function of this optimization problem via a lower bound. And we prove this lower bound is a linear function in the special case that the input is binary. We then apply the linear programming (LP) relaxation approach to obtain an approximate solution to the proposed nonlinear optimization problem. An adaptive branch-and-cut decoding algorithm has also been developed by making use of the ML-certificate property of the LP decoder for deletion channel. It is seen through simulation studies that the proposed decoding algorithm can achieve close-to-optimal bit error rate (BER) decoding performance at moderate computational complexity.

Research on the strategy of optimizing the discipline layout of environmental geosciences under the National Natural Science Foundation of China

Optimizing the discipline layout is an important task for deepening the reform of National Natural Science Foundation of China. The discipline of environmental geosciences (DEG) has a short history and is not perfect in the discipline layout and system framework. The DEG takes the opportunity of optimizing the discipline layout and proactively responses to the top-level strategy of “Habitable Earth-Earth System Science”, initiated by the Department of Earth Sciences. Based on a wide range of strategic research, the establishment background of DEG was reviewed, and the challenges of DEG in terms of research objects, theoretical systems, technical methods, and research paradigms were analyzed. The overall concept of optimizing the discipline layout of DEG was clarified, namely basic disciplines, interdisciplinary disciplines, cutting-edge fields, new technologies and methods, and national needs. Based on the overall concept of the discipline layout, the discipline framework of “four beams and eight pillars” was established. Four basic disciplines constitute the “four beams”: Soil science (D0701), environmental water science (D0702), environmental atmospheric science (D0703) and environmental biology (D0704). Four interdisciplinary disciplines and four cutting-edge fields together constitute the “eight pillars”. The four interdisciplinary disciplines include engineering geological environment and disaster (D0705), environmental geology (D0706), environmental geochemistry (D0707) and ecotoxicology (D0708). The four cutting-edge fields are environmental pollutant behavior and environmental effects (D0709), environment and health risks (D0710), quaternary environment (D0711), environmental information and environment forecast (D0712). New technologies and methods of DEG (D0713) are the support of the discipline. Regional environmental quality and safety (D0714) and environmental protection and sustainable development (D0715) are the major objectives of DEG to serve national needs. Combining the characteristics and advantages of DEG to serve national needs, the connotation of DEG is defined as pollution environment, ecological environment, disaster environment and healthy environment. The existing problems of the discipline application codes were identified, including incomplete code system, unsmooth logical relationship between codes, and unbalanced code level and size. The preliminary adjustment proposals for the application codes were put forward. This study is for related researchers to discuss and promote the high-quality development of DEG.

Сравнительный анализ методов вычисления гравитационной силы частиц при численном моделировании задачи N-тел

One of the main problems of modern codes for solving the N-body problem is their great similarity. The immediate consequence of this is that the usual method of checking the simulation results by comparing independent approaches is hardly possible. The requirement for accurate calculation of gravitational force does not imply the need to use a unique approach. An approximate calculation of gravitational forces between N interacting particles can be used. For example, an approximate method with high accuracy is the fast multipole method (FMM) that requires only &nbsp;operations instead of &nbsp;to calculate the forces all N particles. FMM groups particles into spatially bounded cells and uses intercellular interactions to approximate forces at any position in the receiver cell using the Taylor extension obtained from the multipole extension of the original cell. Using the error estimate of this process it is possible to minimize the calculations while obtaining the relative errors N≳105. The article provides a brief analysis of N-body modeling methods and shows that the FMM approximates the calculation of mutual forces between particles and the problem under consideration is formulated much easier than, for example, in the case of softened gravity.

Generalized Index Coding Problem and Discrete Polymatroids.

The connections between index coding and matroid theory have been well studied in the recent past. Index coding solutions were first connected to multi linear representation of matroids. For vector linear index codes, discrete polymatroids, which can be viewed as a generalization of the matroids, were used. The index coding problem has been generalized recently to accommodate receivers that demand functions of messages and possess functions of messages. In this work we explore the connections between generalized index coding and discrete polymatroids. The conditions that need to be satisfied by a representable discrete polymatroid for a generalized index coding problem to have a vector linear solution is established. From a discrete polymatroid, an index coding problem with coded side information is constructed and it is shown that if the index coding problem has a certain optimal length solution then the discrete polymatroid is representable. If the generalized index coding problem is constructed from a matroid, it is shown that the index coding problem has a binary scalar linear solution of optimal length if and only if the matroid is binary representable.

Cooperative coding and caching scheduling via binary particle swarm optimization in software-defined vehicular networks

With recent development in vehicular communication technologies, much attention has been paid to data dissemination in vehicular networks. In particular, the infrastructure-to-vehicle (I2V) communication is one of the primary technologies to provide a variety of information services. To enhance the bandwidth efficiency of I2V communication, this work considers in a software-defined vehicular networks (SDVN), aiming at exploiting synergistic effects of network coding and vehicular caching. First, we consider a data service scenario in which roadside unites (RSUs) are connected with the controller, which exercises scheduling decisions based on service requests received from vehicles. On this basis, we formulate a cooperative coding and caching scheduling problem with the objective of maximizing the bandwidth efficiency of I2V communication. Then, we propose a binary particle swarm optimization (BPSO)-based coding scheduling (BPSO_CS) algorithm. Finally, we build the simulation model and give a comprehensive performance evaluation. The results conclusively demonstrate the superiority of the proposed solution.

Quantum Reverse Hypercontractivity: Its Tensorization and Application to Strong Converses

In this paper we develop the theory of quantum reverse hypercontractivity inequalities and show how they can be derived from log-Sobolev inequalities. Next we prove a generalization of the Stroock–Varopoulos inequality in the non-commutative setting which allows us to derive quantum hypercontractivity and reverse hypercontractivity inequalities solely from 2-log-Sobolev and 1-log-Sobolev inequalities respectively. We then prove some tensorization-type results providing us with tools to prove hypercontractivity and reverse hypercontractivity not only for certain quantum superoperators but also for their tensor powers. Finally as an application of these results, we generalize a recent technique for proving strong converse bounds in information theory via reverse hypercontractivity inequalities to the quantum setting. We prove strong converse bounds for the problems of quantum hypothesis testing and classical-quantum channel coding based on the quantum reverse hypercontractivity inequalities that we derive.

Advocate for accessibility in historic renovations

Code problems had forced the closing of one of the most prominent buildings on the University of Massachusetts at Amherst campus, the Old Chapel. The university in 2014 hired Finegold Alexander Architects to transform the site, which once served as a library and place of assembly, into a vibrant student center. Finegold Alexander Principal Regan Shields Ives discussed a project that, according to reviewers honoring it with a Boston Society of Architects William D. Smith Memorial Award, “is proof that accessible design and historic buildings do not have to be at odds with each other.”

Prime Fermat numbers and maximum determinant matrix conjecture

Purpose: Solution to the problem of optimizing the determinants of matrices with a modulus of entries &lt; 1. Developing a theory of such matrices based on preliminary research results. Methods: Extreme solutions (in terms of the determinant) are found by minimizing the absolute values of orthogonal matrix elements, and their subsequent classification. Results: Matrices of orders equal to prime Fermat numbers have been found. They are special, as their absolute determinant maximums can be reached on a simple structure. We provide a precise evaluation of the determinant maximum for these matrices and formulate a conjecture about it. We discuss the close relation between the solutions of extremal problems with the limitation on the matrix column orthogonality and without it. It has been shown that relative maximums of orthogonality-limited matrix determinants correspond to absolute maximums of orthogonality-unlimited matrix determinants. We also discuss the ways to build extremal matrix families for the orders equal to Mersenne numbers. Practical relevance: Maximum determinant matrices are used extensively in the problems of error-free coding, compression and masking of video information. Programs for maximum determinant matrix search and a library of constructed matrices are used in the mathematical network “mathscinet.ru” along with executable online algorithms.

Code smell detection using multi-label classification approach

Code smells are characteristics of the software that indicates a code or design problem which can make software hard to understand, evolve, and maintain. There are several code smell detection tools proposed in the literature, but they produce different results. This is because smells are informally defined or subjective in nature. Machine learning techniques help in addressing the issues of subjectivity, which can learn and distinguish the characteristics of smelly and non-smelly source code elements (classes or methods). However, the existing machine learning techniques can only detect a single type of smell in the code element that does not correspond to a real-world scenario as a single element can have multiple design problems (smells). Further, the mechanisms proposed in the literature could not detect code smells by considering the correlation (co-occurrence) among them. To address these shortcomings, we propose and investigate the use of multi-label classification (MLC) methods to detect whether the given code element is affected by multiple smells or not. In this proposal, two code smell datasets available in the literature are converted into a multi-label dataset (MLD). In the MLD, we found that there is a positive correlation between the two smells (long method and feature envy). In the classification phase, the two methods of MLC considered the correlation among the smells and enhanced the performance (on average more than 95% accuracy) for the 10-fold cross-validation with the ten iterations. The findings reported help the researchers and developers in prioritizing the critical code elements for refactoring based on the number of code smells detected.

Engrossing Prosecution of Code Smells Type Identification and Rectification using Machine Learning AdaBoost Classifier

Software code smells are the structural features which reside in a software source code. Code smell detection is an established method to discover the problems in source code and reorganize the inner structure of object-oriented software for improving the quality of such software, particularly in terms of maintainability, reusability and cost minimization. The developer identified where the code smell is identified and rectified within a system is a major challenging issue. The various code smell detection technique has been designed but it failed to classify the code type and minimum rectification cost. In order to perform classification with minimum cost, an efficient technique called Machine Learning Ada-Boost Classifier (MLABC) technique is introduced. The MLABC technique improves the software quality by identifying and rectifying the different types of software code smell in source code. Initially, MLABC technique uses decision tree as base classifier to identify the code smell type. The decision tree is used to classify the code smell type based on the certain rule. After that, the base classifiers are combined to make a strong classifier using adaboost machine learning technique. The output of strong classifier is used to identify the code smell type. Finally, the code smell type rectification is performed by applying the refactoring technique where the code smell is identified with minimum cost and space complexity. Experimental results shows that the proposed MLABC technique improves the software code quality in terms of code smell type identification accuracy, false positive rate, code smell type rectification cost and space complexity with the source code.

Z-Knotted Triangulations of Surfaces

A zigzag in a map (a 2-cell embedding of a connected graph in a connected closed 2-dimensional surface) is a cyclic sequence of edges satisfying the following conditions: (1) any two consecutive edges lie on the same face and have a common vertex, (2) for any three consecutive edges the first and the third edges are disjoint and the face containing the first and the second edges is distinct from the face which contains the second and the third one. A map is z-knotted if it contains a single zigzag. Such maps are closely related to the Gauss code problem and have nice homological properties. We show that every triangulation of a connected closed 2-dimensional surface admits a z-knotted shredding.

AdSherlock: Efficient and Deployable Click Fraud Detection for Mobile Applications

Mobile advertising plays a vital role in the mobile app ecosystem. A major threat to the sustainability of this ecosystem is click fraud, i.e., ad clicks performed by malicious code or automatic bot problems. Existing click fraud detection approaches focus on analyzing the ad requests at the server side. However, such approaches may suffer from high false negatives since the detection can be easily circumvented, e.g., when the clicks are behind proxies or globally distributed. In this paper, we present AdSherlock, an efficient and deployable click fraud detection approach at the client side (inside the application) for mobile apps. AdSherlock splits the computation-intensive operations of click request identification into an offline procedure and an online procedure. In the offline procedure, AdSherlock generates both exact patterns and probabilistic patterns based on URL (Uniform Resource Locator) tokenization. These patterns are used in the online procedure for click request identification and further used for click fraud detection together with an ad request tree model. We implement a prototype of AdSherlock and evaluate its performance using real apps. The online detector is injected into the app executable archive through binary instrumentation. Results show that AdSherlock achieves higher click fraud detection accuracy compared with state of the art, with negligible runtime overhead.

Gradient-descent decoding of one-step majority-logic decodable codes

In this paper, a new low-complexity gradient-descent based iterative majority-logic decoder (GD-MLGD) is proposed for decoding One-Step Majority-Logic Decodable (OSMLD) codes. We give a formulation of the decoding problem of binary OSMLD codes, as a maximization problem of a derivable objective function. The optimization problem is solved using a pseudo gradient-descent algorithm, which performs iteratively an update towards the optimal estimated codeword been transmitted, based on the first-order partial derivatives of each variable calculated in the previous iteration. The proposed decoding scheme achieves a fast convergence to an optimum codeword compared to other decoding techniques reviewed in this paper, at the cost of lower computational complexity. The quantized version (QGD-MLGD) is also proposed in order to further reduce the computational complexity. Simulation results show that the proposed decoding algorithms outperform all the existing majority-logic decoding schemes, and also various gradient-descent based bit-flipping algorithms, and performs nearly close to the belief propagation sum–product (BP-SP) decoding algorithm of LDPC codes, especially for high code lengths, providing an efficient trade-off between performance and decoding complexity. Moreover, the proposed quantized algorithm has shown to perform better than all the existing decoding techniques. The proposed decoding algorithms have shown to be suitable for ultra reliable, low latency and energy-constrained communication systems where both high performances and low-complexity are required.

Kalman Filter Channel Estimation in 2 × 2 and 4 × 4 STBC MIMO-OFDM Systems

Channel estimation is a challenging problem for space time block coding (STBC) multiple-input and multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems in dynamic environments. To handle this problem and improve the system performance, this paper proposes a Kalman filter (KF) based channel estimation method applied to $2\times2$ and $4\times4$ STBC MIMO-OFDM systems. The proposed method based on the dynamic tracking property of KF is well adopted for dynamic channel estimation. First, a new orthogonal space-time codeword is adopted, and the orthogonal pilot sequences are designed to suppress the interference among transmit antennas. Then, the prediction and update characteristics of KF are researched, and the state space model is established for STBC MIMO-OFDM system. Subsequently, the channel state information (CSI) is estimated iteratively according to the KF estimation equation. At last, to further improve the accuracy of KF channel estimation, the threshold is utilized to suppress the noise in the channel impulse response (CIR) estimated by KF method. Simulation results verify that the proposed KF channel estimation method with orthogonal pilots and STBC provides better bit error rate (BER) and normalized mean square error (NMSE) performance compared with other conventional channel estimation methods, and it can be effectively adapted to dynamic multipath propagation conditions with different low and high order modulations.