Code Pairs Research Articles

Universal secure rank-metric coding schemes with optimal communication overheads

We study the problem of reducing the communication overhead from a noisy wire-tap channel or storage system where data is encoded as a matrix, when more columns (or their linear combinations) are available. We present its applications to reducing communication overheads in universal secure linear network coding and secure distributed storage with crisscross errors and erasures and in the presence of a wire-tapper. Our main contribution is a method to transform coding schemes based on linear rank-metric codes, with certain properties, to schemes with lower communication overheads. By applying this method to pairs of Gabidulin codes, we obtain coding schemes with optimal information rate with respect to their security and rank error correction capability, and with universally optimal communication overheads, when n ≤ m, being n and m the number of columns and number of rows, respectively. Moreover, our method can be applied to other families of maximum rank distance codes when n > m. The downside of the method is generally expanding the packet length, but some practical instances come at no cost.

Index Coded PSK Modulation for Prioritized Receivers

A noisy index coding problem (ICP) over additive white Gaussian noise (AWGN) and Rayleigh fading channels is studied. First, a single-input single-output AWGN broadcast channel is considered. For a chosen index code and an arbitrary mapping (of broadcast vectors to phase-shift keying (PSK) signal points), a decision rule for the maximum-likelihood (ML) decoder is derived. The message error performance of a receiver at high signal-to-noise ratio (SNR) is characterized by a parameter called PSK-index coding gain (PSK-ICG) . The PSK-ICG of a receiver is determined by a metric called minimum inter-set distance . For a given ICP with an order of priority among the receivers, and a chosen $2^N$ -PSK constellation, an algorithm to find (index code, mapping) pairs, each of which gives the best performance in terms of PSK-ICG of the receivers, is proposed. No other pair of index code (of length $N$ with $2^N$ broadcast vectors) and mapping can give a better PSK-ICG for the highest priority receiver. Also, given that the highest priority receiver achieves its best performance, the next highest priority receiver achieves its maximum gain possible and so on in the specified order of priority. Next, the noisy ICP over a multiple-input multiple-output (MIMO) Rayleigh fading channel is considered. The receivers are equipped with a single antenna and a server with two antennas. To obtain the diversity gain along with the coding gain, a MIMO scheme that employs space-time coding along with index coded PSK modulation is proposed. For a chosen index code, an arbitrary mapping (of broadcast vectors to PSK signal points), and a $2 \times 1$ MIMO system employing Alamouti code, we derive a decision rule for the ML decoding. We show that for the best coding gain at high SNR, the mapping must maximize the minimum inter-set distance.

Retrieving and classifying instances of source code plagiarism

Automatic detection of source code plagiarism is an important research field for both the commercial software industry and within the research community. Existing methods of plagiarism detection primarily involve exhaustive pairwise document comparison, which does not scale well for large software collections. To achieve scalability, we approach the problem from an information retrieval (IR) perspective. We retrieve a ranked list of candidate documents in response to a pseudo-query representation constructed from each source code document in the collection. The challenge in source code document retrieval is that the standard bag-of-words (BoW) representation model for such documents is likely to result in many false positives being retrieved, because of the use of identical programming language specific constructs and keywords. To address this problem, we make use of an abstract syntax tree (AST) representation of the source code documents. While the IR approach is efficient, it is essentially unsupervised in nature. To further improve its effectiveness, we apply a supervised classifier (pre-trained with features extracted from sample plagiarized source code pairs) on the top ranked retrieved documents. We report experiments on the SOCO-2014 dataset comprising 12K Java source files with almost 1M lines of code. Our experiments confirm that the AST based approach produces significantly better retrieval effectiveness than a standard BoW representation, i.e., the AST based approach is able to identify a higher number of plagiarized source code documents at top ranks in response to a query source code document. The supervised classifier, trained on features extracted from sample plagiarized source code pairs, is shown to effectively filter and thus further improve the ranked list of retrieved candidate plagiarized documents.

Equilibrium Spline Interface ( ESI) for magnetic confinement codes

A compact and comprehensive interface between magneto-hydrodynamic (MHD) equilibrium codes and gyro-kinetic, particle orbit, MHD stability, and transport codes is presented. Its irreducible set of equilibrium data consists of three (in the 2-D case with occasionally one extra in the 3-D case) functions of coordinates and four 1-D radial profiles together with their first and mixed derivatives. The C reconstruction routines, accessible also from FORTRAN, allow the calculation of basis functions and their first derivatives at any position inside the plasma and in its vicinity. After this all vector fields and geometric coefficients, required for the above mentioned types of codes, can be calculated using only algebraic operations with no further interpolation or differentiation. Program summaryProgram Title: ESIProgram Files doi:http://dx.doi.org/10.17632/w6z58s6ntv.1Licensing provisions: GNU General Public License 3 (GPL)Programming language: CSupplementary material:C2esi.c, F2esi.f, demoC.c, demoF.c RZdemoC.c, RZdemoF.f programs for generation the ESI data and demonstration of their use.Nature of problem: In plasma simulations, the equilibrium codes play a fundamental role in supplying the information about magnetic configuration for different more sophisticated plasma problems: stability, transport, particle orbit or gyro-kinetics. At present, there are two extreme approaches to make a choice of output data from numerical equilibria. One of them requires all functions, necessary for the client code, at all necessary positions to be supplied by the equilibrium codes. This approach works only for closely related pairs of codes, making them highly dependent on each other. It requires excessive storage capacities because the required data may not be very smooth. This approach is not-suitable also for the situation when the client codes need physics variables at unpredictable positions inside the plasma.The other approach uses only primitive information from the equilibrium codes, such as coordinates of grid points and a few radial profiles. Then, the client codes generate all the necessary functions from equilibrium data with their own mappers, which use interpolation and numerical differentiation of original data, both causing convergence problems in the client codes.Solution method: The Equilibrium Spline Interface ( ESI), is proposed as a universal buffer between the equilibrium codes and the other plasma physics codes. ESI possesses comprehensive information about magnetic configuration and is able to provide it to magnetic confinement codes in the ready to use form.Additional comments: The main file esiXZ.c with ESI routines is described in the main text. Two (C and FORTRAN) programs C2esi.c, F2esi.f demonstrate the generation of ESI data files. Four other demo programs, linked with esiXZ.c demonstrate the use of the interface in magnetic flux coordinates ( demoC.c, demoF.f) and in laboratory cylindrical coordinates r,z ( RZdemoC.c, RZdemoF.f).

Low-Complexity Soft-Decision Concatenated LDGM-Staircase FEC for High-Bit-Rate Fiber-Optic Communication

A concatenated soft-decision forward error correction (FEC) scheme consisting of an inner low-density generator-matrix (LDGM) code and an outer staircase code is proposed. The soft-decision LDGM code is used for error reduction, while the majority of bit errors are corrected by the low-complexity hard-decision staircase code. Decoding complexity of the concatenated code is quantified by a score based on the number of edges in the LDGM code Tanner graph, the number of decoding iterations, and the number of staircase code decoding operations. The inner LDGM ensemble is designed by solving an optimization problem, which minimizes the product of the average node degree and an estimate of the required number of decoding iterations. A search procedure is used to find the inner and outer code pair with lowest complexity. The design procedure results in a Pareto-frontier characterization of the tradeoff between net coding gain and complexity for the concatenated code. Simulations of code designs at $\text{20}\%$ overhead showed that the proposed scheme achieves net coding gains equivalent to existing soft-decision FEC solutions, with up to $\text{57}\%$ reduction in complexity.

Pilot-based parametric channel estimation algorithm for DCO-OFDM-based visual light communications

Due to wide modulation bandwidth in optical communication, multipath channels may be non-sparse and deteriorate communication performance heavily. Traditional compressive sensing-based channel estimation algorithm cannot be employed in this kind of situation. In this paper, we propose a practical parametric channel estimation algorithm for orthogonal frequency division multiplexing (OFDM)-based visual light communication (VLC) systems based on modified zero correlation code (ZCC) pair that has the impulse-like correlation property. Simulation results show that the proposed algorithm achieves better performances than existing least squares (LS)-based algorithm in both bit error ratio (BER) and frequency response estimation.

Notice of Retraction: Simple colorless long-reach WDM-PON with rayleigh backscattering noise mitigation employing remodulated orthogonal coding

We propose and experimentally demonstrate a novel colorless full-duplex passive optical network architecture with Rayleigh backscattering optical beat interference (OBI) noise mitigation by using orthogonal codes. A pair of orthogonal codes are generated and transmitted from optical line terminal (OLT) to optical network unit (ONU) with the same wavelength, in which, one for downstream signal coding, and the other for the upstream seeding signal. In ONU, the upstream signal is remodulated without erasing the downstream signal. Extra centralized CW light sources and gain-saturation RSOAs are not needed. By using orthogonal codes, the spectral overlap between upstream and downstream signal is reduced, which can mitigate OBI noise significantly. The performance of transmission and power margin are investigated through experiments at different data rates, transmission distances compared with normal on-off keying (OOK) signals. The remodulated upstream signals are correlatively received at OLT with coding gain which is useful in long-reach transmissions. Due to coding gain and OBI noise mitigation, total 4~9dB power margin is achieved for 5Gb/s downstream and 1.25Gb/s upstream with 20km to 70km transmission distances.

Unitary circular code motifs in genomes of eukaryotes

A set X of 20 trinucleotides was identified in genes of bacteria, eukaryotes, plasmids and viruses, which has in average the highest occurrence in reading frame compared to its two shifted frames (Michel, 2015; Arquès and Michel, 1996). This set X has an interesting mathematical property as X is a circular code (Arquès and Michel, 1996). Thus, the motifs from this circular code X, called X motifs, have the property to always retrieve, synchronize and maintain the reading frame in genes. The origin of this circular code X in genes is an open problem since its discovery in 1996. Here, we first show that the unitary circular codes (UCC), i.e. sets of one word, allow to generate unitary circular code motifs (UCC motifs), i.e. a concatenation of the same motif (simple repeats) leading to low complexity DNA. Three classes of UCC motifs are studied here: repeated dinucleotides (D+ motifs), repeated trinucleotides (T+ motifs) and repeated tetranucleotides (T+ motifs). Thus, the D+, T+ and T+ motifs allow to retrieve, synchronize and maintain a frame modulo 2, modulo 3 and modulo 4, respectively, and their shifted frames (1 modulo 2; 1 and 2 modulo 3; 1, 2 and 3 modulo 4 according to the C2, C3 and C4 properties, respectively) in the DNA sequences. The statistical distribution of the D+, T+ and T+ motifs is analyzed in the genomes of eukaryotes. A UCC motif and its comp lementary UCC motif have the same distribution in the eukaryotic genomes. Furthermore, a UCC motif and its complementary UCC motif have increasing occurrences contrary to their number of hydrogen bonds, very significant with the T+ motifs. The longest D+, T+ and T+ motifs in the studied eukaryotic genomes are also given. Surprisingly, a scarcity of repeated trinucleotides (T+ motifs) in the large eukaryotic genomes is observed compared to the D+ and T+ motifs. This result has been investigated and may be explained by two outcomes. Repeated trinucleotides (T+ motifs) are identified in the X motifs of low composition (cardinality less than 10) in the genomes of eukaryotes. Furthermore, identical trinucleotide pairs of the circular code X are preferentially used in the gene sequences of eukaryotes. These two results suggest that the unitary circular codes of trinucleotides may have been involved in the formation of the trinucleotide circular code X. Indeed, repeated trinucleotides in the X motifs in the genomes of eukaryotes may represent an intermediary evolution from repeated trinucleotides of cardinality 1 (T+ motifs) in the genomes of eukaryotes up to the X motifs of cardinality 20 in the gene sequences of eukaryotes.

Refined analysis of RGHWs of code pairs coming from Garcia-Stichtenoth’s second tower

Asymptotically good sequences of ramp secret sharing schemes were given in [5] by using one-point algebraic geometric codes defined from asymptotically good towers of function fields. Their security is given by the relative generalized Hamming weights of the corresponding codes. In this paper we demonstrate how to obtain refined information on the RGHWs when the codimension of the codes is small. For general codimension, we give an improved estimate for the highest RGHW.

Synchronisation algorithm based on zero correlation code pair for OFDM‐based VLC systems

Visible light communication (VLC) system based on orthogonal frequency division multiplexing (OFDM) is promising for its ability to link a huge number of devices with high reliability and low latency. However, OFDM-based VLC systems are very sensitive to the symbol timing offsets. Thus, synchronisation algorithm is very important for OFDM-based VLC system. In this study, the authors first propose zero correlation code pair (ZCC pair) and investigate the periodical impulse-shaped correlation property of ZCC pair. Then the authors propose a novel timing offset estimation algorithm based on ZCC pair. The preamble is processed via peak-to-average power ratio (PAPR) reduction algorithms to overcome the PAPR problem in VLC systems. This algorithm achieves high accuracy and has low synchronisation error probability. The effectiveness of the authors' proposed algorithm has been demonstrated using computer simulation under non-light-of-sight VLC and Gaussian channels. The results show that the authors' algorithm outperforms the Schmidl Cox's and Park's algorithms in terms of synchronisation error probability and mean square error of timing error.

Coded excitation speeds up the detection of the fundamental flexural guided wave in coated tubes

The fundamental flexural guided wave (FFGW) permits ultrasonic assessment of the wall thickness of solid waveguides, such as tubes or, e.g., long cortical bones. Recently, an optical non-contact method was proposed for ultrasound excitation and detection with the aim of facilitating the FFGW reception by suppressing the interfering modes from the soft coating. This technique suffers from low SNR and requires iterative physical scanning across the source-receiver distance for 2D-FFT analysis. This means that SNR improvement achieved by temporal averaging becomes time-consuming (several minutes) which reduces the applicability of the technique, especially in time-critical applications such as clinical quantitative ultrasound. To achieve sufficient SNR faster, an ultrasonic excitation by a base-sequence-modulated Golay code (BSGC, 64-bit code pair) on coated tube samples (1-5 mm wall thickness and 5 mm soft coating layer) was used. This approach improved SNR by 21 dB and speeded up the measurement by a factor of 100 compared to using a classical pulse excitation with temporal averaging. The measurement now took seconds instead of minutes, while the ability to determine the wall thickness of the phantoms was maintained. The technique thus allows rapid noncontacting assessment of the wall thickness in coated solid tubes, such as the human bone.

Blind estimation of pseudo‐random codes in periodic long code direct sequence spread spectrum signals

An estimation method of pseudo-random (PN) codes in the periodic long code direct sequence spread spectrum signals using a pair of spreading code and scrambling code [i.e. long scrambling code direct sequence spread spectrum (LSC-DSSS)] is investigated in this study. Via the investigation of properties of triple correlation function (TCF) of m-sequences, the existence of common peaks in the TCFs of different m-sequences is proved, and the corresponding relationship between common peaks and primitive polynomials is further investigated. Four theorems are proposed as supplements of triple correlation theory and a novel estimation algorithm of the PN codes in LSC-DSSS signals is put forward on the basis of the theorems. With certain carrier frequency and chip rate of spreading code, this algorithm first eliminates the influence of information codes through delay-and-multiply operation. Then the TCF of signal is calculated, and the two PN codes in signal are successfully estimated finally by searching and using the common peak coordinates in the TCF. Simulation results show that the proposed algorithm exhibits excellent performance in estimating PN codes in LSC-DSSS signals.

Good code sets from complementary pairs via symmetrical/antisymmetrical chips

Golay complementary code pairs have the advantage of being biphase codes, available at a variety of lengths, with exact sidelobe cancellation. However, they require transmission at two frequencies or channels. At the receiver, the two codes require reception in their own matched filters. The two matched filter outputs are then added, resulting in complete sidelobe cancellation. However, frequency- or channel-selective fading could result in inexact sidelobe cancellation. This paper introduces a new code constructed from the complementary code pair (A, B) by concatenating them with a gap in between, using one frequency band or one channel. The autocorrelation of this code contains a zero-sidelobe region on either side of the mainlobe and an adjacent region of small cross-correlation sidelobes. This is achieved by having the chips used for A and B satisfy the following two conditions: The two chips are symmetrical/antisymmetrical mirror images of each other and the cross-correlation between them is small-i.e., they are quasiorthogonal in the convolution sense. The symmetry/antisymmetry property results in the zero-sidelobe region, while the quasiorthogonality makes the adjacent region of cross-correlation sidelobes small. Linear frequency-modulated (LFM) and piecewise LFM chips satisfy both the symmetry/ antisymmetry and quasiorthogonality conditions. The symmetry/antisymmetry property is shown to be invariant under frequency-selective fading; therefore, sidelobe cancellation is also fading invariant. Any good code set that satisfies the symmetry/antisymmetry condition could be used as chips with the same Golay complementary code pair to generate a good code set with a zero-sidelobe region and an adjacent region of small cross-correlation sidelobes. Such sets are generated by varying the slope of the LFM and piecewise LFM chips.

MalwareHunt: semantics-based malware diffing speedup by normalized basic block memoization

The key challenge of software reverse engineering is that the source code of the program under investigation is typically not available. Identifying differences between two executable binaries (binary diffing) can reveal valuable information in the absence of source code, such as vulnerability patches, software plagiarism evidence, and malware variant relations. Recently, a new binary diffing method based on symbolic execution and constraint solving has been proposed to look for the code pairs with the same semantics, even though they are ostensibly different in syntactics. Such semantics-based method captures intrinsic differences/similarities of binary code, making it a compelling choice to analyze highly-obfuscated malicious programs. However, due to the nature of symbolic execution, semantics-based binary diffing suffers from significant performance slowdown, hindering it from analyzing large numbers of malware samples. In this paper, we attempt to mitigate the high overhead of semantics-based binary diffing with application to malware lineage inference. We first study the key obstacles that contribute to the performance bottleneck. Then we propose normalized basic block memoization to speed up semantics-based binary diffing. We introduce an union-find set structure that records semantically equivalent basic blocks. Managing the union-find structure during successive comparisons allows direct reuse of previously computed results. Moreover, we utilize a set of enhanced optimization methods to further cut down the invocation numbers of constraint solver. We have implemented our technique, called MalwareHunt, on top of a trace-oriented binary diffing tool and evaluated it on 15 polymorphic and metamorphic malware families. We perform intra-family comparisons for the purpose of malware lineage inference. Our experimental results show that MalwareHuntcan accelerate symbolic execution from 2.8X to 5.3X (with an average 4.1X), and reduce constraint solver invocation by a factor of 3.0X to 6.0X (with an average 4.5X).

Network analysis of human diseases using Korean nationwide claims data

ObjectiveTo investigate disease–disease associations by conducting a network analysis using Korean nationwide claims data. MethodsWe used the claims data from the Health Insurance Review and Assessment Service-National Patient Sample for the year 2011. Among the 2049 disease codes in the claims data, 1154 specific disease codes were used and combined into 795 representative disease codes. We analyzed for 381 representative codes, which had a prevalence of >0.1%. For disease code pairs of a combination of 381 representative disease codes, P values were calculated by using the χ2 test and the degrees of associations were expressed as odds ratios (ORs). ResultsFor 5515 (7.62%) statistically significant disease–disease associations with a large effect size (OR>5), we constructed a human disease network consisting of 369 nodes and 5515 edges. The human disease network shows the distribution of diseases in the disease network and the relationships between diseases or disease groups, demonstrating that diseases are associated with each other, forming a complex disease network. We reviewed 5515 disease–disease associations and classified them according to underlying mechanisms. Several disease–disease associations were identified, but the evidence of these associations is not sufficient and the mechanisms underlying these associations have not been clarified yet. Further research studies are needed to investigate these associations and their underlying mechanisms. ConclusionHuman disease network analysis using claims data enriches the understanding of human diseases and provides new insights into disease–disease associations that can be useful in future research.

On the distance between linear codes

Let V be an n-dimensional vector space over the finite field consisting of q elements and let Γk(V) be the Grassmann graph formed by k-dimensional subspaces of V, 1<k<n−1. Denote by Γ(n,k)q the restriction of Γk(V) to the set of all non-degenerate linear [n,k]q codes. We show that for any two codes the distance in Γ(n,k)q coincides with the distance in Γk(V) only in the case when n<(q+1)2+k−2, i.e. if n is sufficiently large then for some pairs of codes the distances in the graphs Γk(V) and Γ(n,k)q are distinct. We describe one class of such pairs.

Technological novelty profile and invention’s future impact

We consider inventions as novel combinations of existing technological capabilities. Patent data allow us to explicitly identify such combinatorial processes in invention activities. Unconsidered in the previous research, not every new combination is novel to the same extent. Some combinations are naturally anticipated based on patent activities in the past or mere random choices, and some appear to deviate exceptionally from existing invention pathways. We calculate a relative likelihood that each pair of classification codes is put together at random, and a deviation from the empirical observation so as to assess the overall novelty (or conventionality) that the patent brings forth at each year. An invention is considered as unconventional if a pair of codes therein is unlikely to be used together given the statistics in the past. Temporal evolution of the distribution indicates that the patenting activities become more conventional with occasional cross-over combinations. Our analyses show that patents introducing novelty on top of the conventional units would receive higher citations, and hence have higher impact.

Colorless Long-Reach Duplex WDM-PON With Rayleigh Backscattering Noise Mitigation Using Orthogonal Codes

We propose and experimentally demonstrate a novel colorless full-duplex passive optical network (PON) access architecture. Utilizing orthogonal codes and correlation receiving methods, the novel PON can mitigate the optical beat interference (OBI) noise induced by Rayleigh backscattering (RB). A pair of electrical orthogonal codes is generated and modulated at the same wavelength in the optical line terminal (OLT). Then, modulated optical signals are transmitted from the OLT to the optical network units (ONUs). One of the codes is for downstream signal coding, and the other is used as the upstream seed. In the ONU, the upstream signal is remodulated without erasing the downstream signal. Neither extra centralized continuous wave (CW) light sources nor gain-saturated reflective semiconductor optical amplifier is required. By using these orthogonal codes, the spectral overlap between upstream signal and downstream signal in the full-duplex system is reduced, which can mitigate the OBI noise significantly. The performance of transmission and power margin is investigated through the experiments with different transmission distances. The remodulated upstream signals are recovered by correlation algorithm in the OLT. By correlation algorithm, we can get coding gain, which is important in long-reach transmissions. Because of coding gain and the OBI noise mitigation, a link power margin of 4-10 dB can be achieved for 5 Gb/s downstream and 1.25 Gb/s upstream, when the transmission distance is from 20 to 70 km.

Image Encryption Algorithm Based on Dynamic DNA Coding and Chen’s Hyperchaotic System

With the development of national information processes, specific image information from secret departments or individuals is often required to be confidentially transmitted. Numerous image encryption methods exist, especially since the initial value sensitivity and other characteristics of chaos theory and chaos theory-based encryption have become increasingly important in recent years. At present, DNA coding constitutes a new research direction of image encryption that uses the four base pairs of DNA code and image pixel values to establish a special correspondence, in order to achieve pixel diffusion. There are eight DNA encoding rules, and current methods of selecting the DNA encoding rules are largely fixed. Thus, the security of encoded data is not high. In this paper, we use the Lorenz chaotic system, Chen’s hyperchaotic system, and the DNA encoding combination and present a new image encryption algorithm that can dynamically select eight types of DNA encoding rules and eight types of DNA addition and subtraction rules, with significant improvements in security. Through simulation experiments and histograms, correlations, and NPCR analyses, we have determined that the algorithm possesses numerous desirable features, including good encryption effects and antishear and antinoise performances.

Critical Pairs for the Product Singleton Bound

We characterize Product-MDS pairs of linear codes, i.e.\ pairs of codes $C,D$ whose product under coordinatewise multiplication has maximum possible minimum distance as a function of the code length and the dimensions $\dim C, \dim D$. We prove in particular, for $C=D$, that if the square of the code $C$ has minimum distance at least $2$, and $(C,C)$ is a Product-MDS pair, then either $C$ is a generalized Reed-Solomon code, or $C$ is a direct sum of self-dual codes. In passing we establish coding-theory analogues of classical theorems of additive combinatorics.