OpenRaiser/Intern-Atlas huggingface dataset:
Duality of Channel Encoding and Decoding - Part I: Rate-1 Binary Convolutional Codes
Venue: arXiv cs.IT 2016
Year: 2016

In this paper, we revisit the forward, backward and bidirectional Bahl-Cocke-Jelinek-Raviv (BCJR) soft-input soft-output (SISO) maximum a posteriori probability (MAP) decoding process of rate-1 binary convolutional codes. From this we establish some interesting explicit relationships between encoding and decoding of rate-1 convolutional codes. We observe that the forward and backward BCJR SISO MAP decoders can be simply represented by their dual SISO channel encoders using shift registers in the complex number field. Similarly, the bidirectional MAP decoding can be implemented by linearly combining the shift register contents of the dual SISO encoders of the respective forward and backward decoders. The dual encoder structures for various recursive and non-recursive rate-1 convolutional codes are derived.
Turing machines can be efficiently simulated by the General Purpose Analog Computer
Venue: arXiv cs.CC 2016
Year: 2016

The Church-Turing thesis states that any sufficiently powerful computational model which captures the notion of algorithm is computationally equivalent to the Turing machine. This equivalence usually holds both at a computability level and at a computational complexity level modulo polynomial reductions. However, the situation is less clear in what concerns models of computation using real numbers, and no analog of the Church-Turing thesis exists for this case. Recently it was shown that some models of computation with real numbers were equivalent from a computability perspective. In particular it was shown that Shannon's General Purpose Analog Computer (GPAC) is equivalent to Computable Analysis. However, little is known about what happens at a computational complexity level. In this paper we shed some light on the connections between this two models, from a computational complexity level, by showing that, modulo polynomial reductions, computations of Turing machines can be simulated by GPACs, without the need of using more (space) resources than those used in the original Turing computation, as long as we are talking about bounded computations. In other words, computations done by the GPAC are as space-efficient as computations done in the context of Computable Analysis.
Coalescing random walks and voting on connected graphs
Venue: arXiv cs.DS 2016
Year: 2016

In a coalescing random walk, a set of particles make independent random walks on a graph. Whenever one or more particles meet at a vertex, they unite to form a single particle, which then continues the random walk through the graph. Coalescing random walks can be used to achieve consensus in distributed networks, and is the basis of the self-stabilizing mutual exclusion algorithm of Israeli and Jalfon. Let G=(V,E), be an undirected, connected n vertex graph with m edges. Let C(n) be the expected time for all particles to coalesce, when initially one particle is located at each vertex of an n vertex graph. We study the problem of bounding the coalescence time C(n) for general classes of graphs. Our main result is that C(n)= O(1/(1-lambda_2))*((log n)^4 +n/A)), where lambda_2 is the absolute value of the second largest eigenvalue of the transition matrix of the random walk, A= (sum d^2(v))/(d^2 n), d(v) is the degree of vertex v, and d is the average node degree. The parameter A is an indicator of the variability of node degrees. Thus 1 <= A =O(n), with A=1 for regular graphs.
Towards the Evolution of Vertical-Axis Wind Turbines using Supershapes
Venue: arXiv cs.NE 2016
Year: 2016

We have recently presented an initial study of evolutionary algorithms used to design vertical-axis wind turbines (VAWTs) wherein candidate prototypes are evaluated under approximated wind tunnel conditions after being physically instantiated by a 3D printer. That is, unlike other approaches such as computational fluid dynamics simulations, no mathematical formulations are used and no model assumptions are made. However, the representation used significantly restricted the range of morphologies explored. In this paper, we present initial explorations into the use of a simple generative encoding, known as Gielis superformula, that produces a highly flexible 3D shape representation to design VAWT. First, the target-based evolution of 3D artefacts is investigated and subsequently initial design experiments are performed wherein each VAWT candidate is physically instantiated and evaluated under approximated wind tunnel conditions. It is shown possible to produce very closely matching designs of a number of 3D objects through the evolution of supershapes produced by Gielis superformula. Moreover, it is shown possible to use artificial physical evolution to identify novel and increasingly efficient supershape VAWT designs.
Spectral Graph Cut from a Filtering Point of View
Venue: arXiv cs.CV 2016
Year: 2016

Spectral graph theory is well known and widely used in computer vision. In this paper, we analyze image segmentation algorithms that are based on spectral graph theory, e.g., normalized cut, and show that there is a natural connection between spectural graph theory based image segmentationand and edge preserving filtering. Based on this connection we show that the normalized cut algorithm is equivalent to repeated iterations of bilateral filtering. Then, using this equivalence we present and implement a fast normalized cut algorithm for image segmentation. Experiments show that our implementation can solve the original optimization problem in the normalized cut algorithm 10 to 100 times faster. Furthermore, we present a new algorithm called conditioned normalized cut for image segmentation that can easily incorporate color image patches and demonstrate how this segmentation problem can be solved with edge preserving filtering.
Cyclic Codes from Dickson Polynomials
Venue: arXiv cs.IT 2016
Year: 2016

Due to their efficient encoding and decoding algorithms cyclic codes, a subclass of linear codes, have applications in consumer electronics, data storage systems, and communication systems. In this paper, Dickson polynomials of the first and second kind over finite fields are employed to construct a number of classes of cyclic codes. Lower bounds on the minimum weight of some classes of the cyclic codes are developed. The minimum weights of some other classes of the codes constructed in this paper are determined. The dimensions of the codes obtained in this paper are flexible. Most of the codes presented in this paper are optimal or almost optimal in the sense that they meet some bound on linear codes. Over ninety cyclic codes of this paper should be used to update the current database of tables of best linear codes known. Among them sixty are optimal in the sense that they meet some bound on linear codes and the rest are cyclic codes having the same parameters as the best linear code in the current database maintained at http://www.codetables.de/.
The Space Complexity of 2-Dimensional Approximate Range Counting
Venue: arXiv cs.DS 2016
Year: 2016

We study the problem of $2$-dimensional orthogonal range counting with additive error. Given a set $P$ of $n$ points drawn from an $n\times n$ grid and an error parameter $\eps$, the goal is to build a data structure, such that for any orthogonal range $R$, it can return the number of points in $P\cap R$ with additive error $\eps n$. A well-known solution for this problem is the {\em $\eps$-approximation}, which is a subset $A\subseteq P$ that can estimate the number of points in $P\cap R$ with the number of points in $A\cap R$. It is known that an $\eps$-approximation of size $O(\frac{1}{\eps} \log^{2.5} \frac{1}{\eps})$ exists for any $P$ with respect to orthogonal ranges, and the best lower bound is $Ω(\frac{1}{\eps} \log \frac{1}{\eps})$. The $\eps$-approximation is a rather restricted data structure, as we are not allowed to store any information other than the coordinates of the points in $P$. In this paper, we explore what can be achieved without any restriction on the data structure. We first describe a simple data structure that uses $O(\frac{1}{\eps}(\log^2\frac{1} {\eps} + \log n) )$ bits and answers queries with error $\eps n$. We then prove a lower bound that any data structure that answers queries with error $\eps n$ must use $Ω(\frac{1}{\eps}(\log^2\frac{1} {\eps} + \log n) )$ bits. Our lower bound is information-theoretic: We show that there is a collection of $2^{Ω(n\log n)}$ point sets with large {\em union combinatorial discrepancy}, and thus are hard to distinguish unless we use $Ω(n\log n)$ bits.
Breaking a chaotic image encryption algorithm based on modulo addition and XOR operation
Venue: arXiv cs.CR 2016
Year: 2016

This paper re-evaluates the security of a chaotic image encryption algorithm called MCKBA/HCKBA and finds that it can be broken efficiently with two known plain-images and the corresponding cipher-images. In addition, it is reported that a previously proposed breaking on MCKBA/HCKBA can be further improved by reducing the number of chosen plain-images from four to two. The two attacks are both based on the properties of solving a composite function involving the carry bit, which is composed of the modulo addition and the bitwise OR operations. Both rigorous theoretical analysis and detailed experimental results are provided.
History-Register Automata
Venue: arXiv cs.PL 2016
Year: 2016

Programs with dynamic allocation are able to create and use an unbounded number of fresh resources, such as references, objects, files, etc. We propose History-Register Automata (HRA), a new automata-theoretic formalism for modelling such programs. HRAs extend the expressiveness of previous approaches and bring us to the limits of decidability for reachability checks. The distinctive feature of our machines is their use of unbounded memory sets (histories) where input symbols can be selectively stored and compared with symbols to follow. In addition, stored symbols can be consumed or deleted by reset. We show that the combination of consumption and reset capabilities renders the automata powerful enough to imitate counter machines, and yields closure under all regular operations apart from complementation. We moreover examine weaker notions of HRAs which strike different balances between expressiveness and effectiveness.
A partition of the hypercube into maximally nonparallel Hamming codes
Venue: arXiv cs.IT 2016
Year: 2016

By using the Gold map, we construct a partition of the hypercube into cosets of Hamming codes such that for every two cosets the corresponding Hamming codes are maximally nonparallel, that is, their intersection cardinality is as small as possible to admit nonintersecting cosets.
A Unifying Variational Perspective on Some Fundamental Information Theoretic Inequalities
Venue: arXiv cs.IT 2016
Year: 2016

This paper proposes a unifying variational approach for proving and extending some fundamental information theoretic inequalities. Fundamental information theory results such as maximization of differential entropy, minimization of Fisher information (Cramér-Rao inequality), worst additive noise lemma, entropy power inequality (EPI), and extremal entropy inequality (EEI) are interpreted as functional problems and proved within the framework of calculus of variations. Several applications and possible extensions of the proposed results are briefly mentioned.
Model-Checking of Linear-Time Properties in Multi-Valued Systems
Venue: arXiv cs.LO 2016
Year: 2016

In this paper, we study model-checking of linear-time properties in multi-valued systems. Safety property, invariant property, liveness property, persistence and dual-persistence properties in multi-valued logic systems are introduced. Some algorithms related to the above multi-valued linear-time properties are discussed. The verification of multi-valued regular safety properties and multi-valued $ω$-regular properties using lattice-valued automata are thoroughly studied. Since the law of non-contradiction (i.e., $a\wedge \neg a=0$) and the law of excluded-middle (i.e., $a\vee \neg a=1$) do not hold in multi-valued logic, the linear-time properties introduced in this paper have the new forms compared to those in classical logic. Compared to those classical model checking methods, our methods to multi-valued model checking are more directly accordingly. A new form of multi-valued model checking with membership degree is also introduced. In particular, we show that multi-valued model-checking can be reduced to the classical model checking. The related verification algorithms are also presented. Some illustrative examples and case study are also provided.
Factorization of Z-homogeneous polynomials in the First (q)-Weyl Algebra
Venue: arXiv cs.SC 2016
Year: 2016

We present algorithms to factorize weighted homogeneous elements in the first polynomial Weyl algebra and $q$-Weyl algebra, which are both viewed as a $\mathbb{Z}$-graded rings. We show, that factorization of homogeneous polynomials can be almost completely reduced to commutative univariate factorization over the same base field with some additional uncomplicated combinatorial steps. This allows to deduce the complexity of our algorithms in detail. Furthermore, we will show for homogeneous polynomials that irreducibility in the polynomial first Weyl algebra also implies irreducibility in the rational one, which is of interest for practical reasons. We report on our implementation in the computer algebra system \textsc{Singular}. It outperforms for homogeneous polynomials currently available implementations dealing with factorization in the first Weyl algebra both in speed and elegancy of the results.
A New Access Control Scheme for Facebook-style Social Networks
Venue: arXiv cs.CR 2016
Year: 2016

The popularity of online social networks (OSNs) makes the protection of users' private information an important but scientifically challenging problem. In the literature, relationship-based access control schemes have been proposed to address this problem. However, with the dynamic developments of OSNs, we identify new access control requirements which cannot be fully captured by the current schemes. In this paper, we focus on public information in OSNs and treat it as a new dimension which users can use to regulate access to their resources. We define a new OSN model containing users and their relationships as well as public information. Based on this model, we introduce a variant of hybrid logic for formulating access control policies. We exploit a type of category information and relationship hierarchy to further extend our logic for its usage in practice. In the end, we propose a few solutions to address the problem of information reliability in OSNs, and formally model collaborative access control in our access control scheme.
Optimal Stochastic Strongly Convex Optimization with a Logarithmic Number of Projections
Venue: arXiv cs.LG 2016
Year: 2016

We consider stochastic strongly convex optimization with a complex inequality constraint. This complex inequality constraint may lead to computationally expensive projections in algorithmic iterations of the stochastic gradient descent~(SGD) methods. To reduce the computation costs pertaining to the projections, we propose an Epoch-Projection Stochastic Gradient Descent~(Epro-SGD) method. The proposed Epro-SGD method consists of a sequence of epochs; it applies SGD to an augmented objective function at each iteration within the epoch, and then performs a projection at the end of each epoch. Given a strongly convex optimization and for a total number of $T$ iterations, Epro-SGD requires only $\log(T)$ projections, and meanwhile attains an optimal convergence rate of $O(1/T)$, both in expectation and with a high probability. To exploit the structure of the optimization problem, we propose a proximal variant of Epro-SGD, namely Epro-ORDA, based on the optimal regularized dual averaging method. We apply the proposed methods on real-world applications; the empirical results demonstrate the effectiveness of our methods.
Measuring Transport Difficulty of Data Dissemination in Large-Scale Online Social Networks: An Interest-Driven Case
Venue: arXiv cs.SI 2016
Year: 2016

In this paper, we aim to model the formation of data dissemination in online social networks (OSNs), and measure the transport difficulty of generated data traffic. We focus on a usual type of interest-driven social sessions in OSNs, called \emph{Social-InterestCast}, under which a user will autonomously determine whether to view the content from his followees depending on his interest. It is challenging to figure out the formation mechanism of such a Social-InterestCast, since it involves multiple interrelated factors such as users' social relationships, users' interests, and content semantics. We propose a four-layered system model, consisting of physical layer, social layer, content layer, and session layer. By this model we successfully obtain the geographical distribution of Social-InterestCast sessions, serving as the precondition for quantifying data transport difficulty. We define the fundamental limit of \emph{transport load} as a new metric, called \emph{transport complexity}, i.e., the \emph{minimum required} transport load for an OSN over a given carrier network. Specifically, we derive the transport complexity for Social-InterestCast sessions in a large-scale OSN over the carrier network with optimal communication architecture. The results can act as the common lower bounds on transport load for Social-InterestCast over any carrier networks. To the best of our knowledge, this is the first work to measure the transport difficulty for data dissemination in OSNs by modeling session patterns with the interest-driven characteristics.
Cut-Set Bounds on Network Information Flow
Venue: arXiv cs.IT 2016
Year: 2016

Explicit characterization of the capacity region of communication networks is a long standing problem. While it is known that network coding can outperform routing and replication, the set of feasible rates is not known in general. Characterizing the network coding capacity region requires determination of the set of all entropic vectors. Furthermore, computing the explicitly known linear programming bound is infeasible in practice due to an exponential growth in complexity as a function of network size. This paper focuses on the fundamental problems of characterization and computation of outer bounds for networks with correlated sources. Starting from the known local functional dependencies induced by the communications network, we introduce the notion of irreducible sets, which characterize implied functional dependencies. We provide recursions for computation of all maximal irreducible sets. These sets act as information-theoretic bottlenecks, and provide an easily computable outer bound. We extend the notion of irreducible sets (and resulting outer bound) for networks with independent sources. We compare our bounds with existing bounds in the literature. We find that our new bounds are the best among the known graph theoretic bounds for networks with correlated sources and for networks with independent sources.
Simulation of a Channel with Another Channel
Venue: arXiv cs.IT 2016
Year: 2016

In this paper, we study the problem of simulating a DMC channel from another DMC channel under an average-case and an exact model. We present several achievability and infeasibility results, with tight characterizations in special cases. In particular for the exact model, we fully characterize when a BSC channel can be simulated from a BEC channel when there is no shared randomness. We also provide infeasibility and achievability results for simulation of a binary channel from another binary channel in the case of no shared randomness. To do this, we use properties of Rényi capacity of a given order. We also introduce a notion of "channel diameter" which is shown to be additive and satisfy a data processing inequality.
Joint Unitary Triangularization for Gaussian Multi-User MIMO Networks
Venue: arXiv cs.IT 2016
Year: 2016

The problem of transmitting a common message to multiple users over the Gaussian multiple-input multiple-output broadcast channel is considered, where each user is equipped with an arbitrary number of antennas. A closed-loop scenario is assumed, for which a practical capacity-approaching scheme is developed. By applying judiciously chosen unitary operations at the transmit and receive nodes, the channel matrices are triangularized so that the resulting matrices have equal diagonals, up to a possible multiplicative scalar factor. This, along with the utilization of successive interference cancellation, reduces the coding and decoding tasks to those of coding and decoding over the single-antenna additive white Gaussian noise channel. Over the resulting effective channel, any off-the-shelf code may be used. For the two-user case, it was recently shown that such joint unitary triangularization is always possible. In this paper, it is shown that for more than two users, it is necessary to carry out the unitary linear processing jointly over multiple channel uses, i.e., space-time processing is employed. It is further shown that exact triangularization, where all resulting diagonals are equal, is still not always possible, and appropriate conditions for the existence of such are established for certain cases. When exact triangularization is not possible, an asymptotic construction is proposed, that achieves the desired property of equal diagonals up to edge effects that can be made arbitrarily small, at the price of processing a sufficiently large number of channel uses together.
Persian Heritage Image Binarization Competition (PHIBC 2012)
Venue: arXiv cs.CV 2016
Year: 2016

The first competition on the binarization of historical Persian documents and manuscripts (PHIBC 2012) has been organized in conjunction with the first Iranian conference on pattern recognition and image analysis (PRIA 2013). The main objective of PHIBC 2012 is to evaluate performance of the binarization methodologies, when applied on the Persian heritage images. This paper provides a report on the methodology and performance of the three submitted algorithms based on evaluation measures has been used.
Achieving the Uniform Rate Region of General Multiple Access Channels by Polar Coding
Venue: arXiv cs.IT 2016
Year: 2016

We consider the problem of polar coding for transmission over $m$-user multiple access channels. In the proposed scheme, all users encode their messages using a polar encoder, while a multi-user successive cancellation decoder is deployed at the receiver. The encoding is done separately across the users and is independent of the target achievable rate. For the code construction, the positions of information bits and frozen bits for each of the users are decided jointly. This is done by treating the polar transformations across all the $m$ users as a single polar transformation with a certain \emph{polarization base}. We characterize the resolution of achievable rates on the dominant face of the uniform rate region in terms of the number of users $m$ and the length of the polarization base $L$. In particular, we prove that for any target rate on the dominant face, there exists an achievable rate, also on the dominant face, within the distance at most $\frac{(m-1)\sqrt{m}}{L}$ from the target rate. We then prove that the proposed MAC polar coding scheme achieves the whole uniform rate region with fine enough resolution by changing the decoding order in the multi-user successive cancellation decoder, as $L$ and the code block length $N$ grow large. The encoding and decoding complexities are $O(N \log N)$ and the asymptotic block error probability of $O(2^{-N^{0.5 - ε}})$ is guaranteed. Examples of achievable rates for the $3$-user multiple access channel are provided.