Showing papers on "Concatenation published in 2019"

F3Net: Fusion, Feedback and Focus for Salient Object Detection

Abstract: Most of existing salient object detection models have achieved great progress by aggregating multi-level features extracted from convolutional neural networks. However, because of the different receptive fields of different convolutional layers, there exists big differences between features generated by these layers. Common feature fusion strategies (addition or concatenation) ignore these differences and may cause suboptimal solutions. In this paper, we propose the F3Net to solve above problem, which mainly consists of cross feature module (CFM) and cascaded feedback decoder (CFD) trained by minimizing a new pixel position aware loss (PPA). Specifically, CFM aims to selectively aggregate multi-level features. Different from addition and concatenation, CFM adaptively selects complementary components from input features before fusion, which can effectively avoid introducing too much redundant information that may destroy the original features. Besides, CFD adopts a multi-stage feedback mechanism, where features closed to supervision will be introduced to the output of previous layers to supplement them and eliminate the differences between features. These refined features will go through multiple similar iterations before generating the final saliency maps. Furthermore, different from binary cross entropy, the proposed PPA loss doesn't treat pixels equally, which can synthesize the local structure information of a pixel to guide the network to focus more on local details. Hard pixels from boundaries or error-prone parts will be given more attention to emphasize their importance. F3Net is able to segment salient object regions accurately and provide clear local details. Comprehensive experiments on five benchmark datasets demonstrate that F3Net outperforms state-of-the-art approaches on six evaluation metrics.

Semantic Sentence Matching with Densely-connected Recurrent and Co-attentive Information

Abstract: Sentence matching is widely used in various natural language tasks such as natural language inference, paraphrase identification, and question answering. For these tasks, understanding logical and semantic relationship between two sentences is required but it is yet challenging. Although attention mechanism is useful to capture the semantic relationship and to properly align the elements of two sentences, previous methods of attention mechanism simply use a summation operation which does not retain original features enough. Inspired by DenseNet, a densely connected convolutional network, we propose a densely-connected co-attentive recurrent neural network, each layer of which uses concatenated information of attentive features as well as hidden features of all the preceding recurrent layers. It enables preserving the original and the co-attentive feature information from the bottommost word embedding layer to the uppermost recurrent layer. To alleviate the problem of an ever-increasing size of feature vectors due to dense concatenation operations, we also propose to use an autoencoder after dense concatenation. We evaluate our proposed architecture on highly competitive benchmark datasets related to sentence matching. Experimental results show that our architecture, which retains recurrent and attentive features, achieves state-of-the-art performances for most of the tasks.

Guided Image-to-Image Translation With Bi-Directional Feature Transformation

Abstract: We address the problem of guided image-to-image translation where we translate an input image into another while respecting the constraints provided by an external, user-provided guidance image. Various types of conditioning mechanisms for leveraging the given guidance image have been explored, including input concatenation, feature concatenation, and conditional affine transformation of feature activations. All these conditioning mechanisms, however, are uni-directional, i.e., no information flow from the input image back to the guidance. To better utilize the constraints of the guidance image, we present a bi-directional feature transformation (bFT) scheme. We show that our novel bFT scheme outperforms other conditioning schemes and has comparable results to state-of-the-art methods on different tasks.

Deep Reinforcement Learning for Swarm Systems

Abstract: Recently, deep reinforcement learning (RL) methods have been applied successfully to multi-agent scenarios. Typically, the observation vector for decentralized decision making is represented by a concatenation of the (local) information an agent gathers about other agents. However, concatenation scales poorly to swarm systems with a large number of homogeneous agents as it does not exploit the fundamental properties inherent to these systems: (i) the agents in the swarm are interchangeable and (ii) the exact number of agents in the swarm is irrelevant. Therefore, we propose a new state representation for deep multi-agent RL based on mean embeddings of distributions, where we treat the agents as samples and use the empirical mean embedding as input for a decentralized policy. We define different feature spaces of the mean embedding using histograms, radial basis functions and neural networks trained end-to-end. We evaluate the representation on two well-known problems from the swarm literature in a globally and locally observable setup. For the local setup we furthermore introduce simple communication protocols. Of all approaches, the mean embedding representation using neural network features enables the richest information exchange between neighboring agents, facilitating the development of complex collective strategies.

Decision procedures for path feasibility of string-manipulating programs with complex operations

Abstract: The design and implementation of decision procedures for checking path feasibility in string-manipulating programs is an important problem, with such applications as symbolic execution of programs with strings and automated detection of cross-site scripting (XSS) vulnerabilities in web applications. A (symbolic) path is given as a finite sequence of assignments and assertions (i.e. without loops), and checking its feasibility amounts to determining the existence of inputs that yield a successful execution. Modern programming languages (e.g. JavaScript, PHP, and Python) support many complex string operations, and strings are also often implicitly modified during a computation in some intricate fashion (e.g. by some autoescaping mechanisms). In this paper we provide two general semantic conditions which together ensure the decidability of path feasibility: (1) each assertion admits regular monadic decomposition (i.e. is an effectively recognisable relation), and (2) each assignment uses a (possibly nondeterministic) function whose inverse relation preserves regularity. We show that the semantic conditions are expressive since they are satisfied by a multitude of string operations including concatenation, one-way and two-way finite-state transducers, replaceall functions (where the replacement string could contain variables), string-reverse functions, regular-expression matching, and some (restricted) forms of letter-counting/length functions. The semantic conditions also strictly subsume existing decidable string theories (e.g. straight-line fragments, and acyclic logics), and most existing benchmarks (e.g. most of Kaluza’s, and all of SLOG’s, Stranger’s, and SLOTH’s benchmarks). Our semantic conditions also yield a conceptually simple decision procedure, as well as an extensible architecture of a string solver in that a user may easily incorporate his/her own string functions into the solver by simply providing code for the pre-image computation without worrying about other parts of the solver. Despite these, the semantic conditions are unfortunately too general to provide a fast and complete decision procedure. We provide strong theoretical evidence for this in the form of complexity results. To rectify this problem, we propose two solutions. Our main solution is to allow only partial string functions (i.e., prohibit nondeterminism) in condition (2). This restriction is satisfied in many cases in practice, and yields decision procedures that are effective in both theory and practice. Whenever nondeterministic functions are still needed (e.g. the string function split), our second solution is to provide a syntactic fragment that provides a support of nondeterministic functions, and operations like one-way transducers, replaceall (with constant replacement string), the string-reverse function, concatenation, and regular-expression matching. We show that this fragment can be reduced to an existing solver SLOTH that exploits fast model checking algorithms like IC3. We provide an efficient implementation of our decision procedure (assuming our first solution above, i.e., deterministic partial string functions) in a new string solver OSTRICH. Our implementation provides built-in support for concatenation, reverse, functional transducers (FFT), and replaceall and provides a framework for extensibility to support further string functions. We demonstrate the efficacy of our new solver against other competitive solvers.

Capacity Results for the Noisy Shuffling Channel

Abstract: Motivated by DNA-based storage, we study the noisy shuffling channel, which can be seen as the concatenation of a standard noisy channel (such as the BSC) and a shuffling channel, which breaks the data block into small pieces and shuffles them. This channel models a DNA storage system, by capturing two of its key aspects: (1) the data is written onto many short DNA molecules that are stored in an unordered way and (2) the molecules are corrupted by noise at synthesis, sequencing, and during storage. For the BSC-shuffling channel we characterize the capacity exactly (for a large set of parameters), and show that a simple index-based coding scheme is optimal.

Improved Fault Size Estimation Method for Rolling Element Bearings Based on Concatenation Dictionary

Abstract: This paper offers a new perspective on the vibrations of discrete bearing faults by focusing on the micro-motion states of rolling elements in spall fault bearings and proposes an improved matching pursuit algorithm for quantitative diagnosis with a high accuracy of atom selection and calculation efficiency. The generation mechanism of the vibration response signal is explained by analyzing the micro-motion status when rolling elements passing through the spall. A concatenation dictionary composed of an impact dictionary as the higher level and step dictionary as the lower level is constructed based on the acceleration variation analysis of the rolling elements. The information output by the higher-level dictionary is used as the input information for the lower-level dictionary to extract the fault features. Only one iteration on the higher-level dictionary is necessary to extract the correct impact atoms, with all subsequent iterative steps assigned to the lower-level dictionary. The advantage is that the influence of high-energy impact components on the extraction of step atoms can be removed. Thereafter, the optimized algorithm based on the concatenation dictionary is applied to the analysis of simulation and experimental signals. The comparative analysis demonstrates that the effective quantitative diagnosis is obtained, while the diagnostic precision and calculation efficiency are improved.

On the Complexity of String Matching for Graphs

Abstract: Exact string matching in labeled graphs is the problem of searching paths of a graph G=(V,E) such that the concatenation of their node labels is equal to the given pattern string P[1..m]. This basic problem can be found at the heart of more complex operations on variation graphs in computational biology, of query operations in graph databases, and of analysis operations in heterogeneous networks. We prove a conditional lower bound stating that, for any constant epsilon>0, an O(|E|^{1 - epsilon} m)-time, or an O(|E| m^{1 - epsilon})-time algorithm for exact string matching in graphs, with node labels and patterns drawn from a binary alphabet, cannot be achieved unless the Strong Exponential Time Hypothesis (SETH) is false. This holds even if restricted to undirected graphs with maximum node degree two, i.e. to zig-zag matching in bidirectional strings, or to deterministic directed acyclic graphs whose nodes have maximum sum of indegree and outdegree three. These restricted cases make the lower bound stricter than what can be directly derived from related bounds on regular expression matching (Backurs and Indyk, FOCS'16). In fact, our bounds are tight in the sense that lowering the degree or the alphabet size yields linear-time solvable problems. An interesting corollary is that exact and approximate matching are equally hard (quadratic time) in graphs under SETH. In comparison, the same problems restricted to strings have linear-time vs quadratic-time solutions, respectively (approximate pattern matching having also a matching SETH lower bound (Backurs and Indyk, STOC'15)).

Biomedical image classification based on a feature concatenation and ensemble of deep CNNs

Abstract: Deep learning and more specifically Convolutional Neural Network (CNN) is a cutting edge technique which has been applied to many fields including biomedical image classification. To further improve the classification performance for biomedical images, in this paper, a feature concatenation method and a feature concatenation and ensemble method are proposed to combine several CNNs with different depths and structures. Three datasets, namely 2D Hela dataset, PAP smear dataset, and Hep-2 cell image dataset, are used as benchmarks for testing the proposed methods. It is shown from experiments that the feature concatenation and ensemble method outperforms each individual CNN, and the feature concatenation method, as well as several state-of-the-art methods in terms of classification accuracy.

Information Aggregation for Multi-Head Attention with Routing-by-Agreement.

Abstract: Multi-head attention is appealing for its ability to jointly extract different types of information from multiple representation subspaces. Concerning the information aggregation, a common practice is to use a concatenation followed by a linear transformation, which may not fully exploit the expressiveness of multi-head attention. In this work, we propose to improve the information aggregation for multi-head attention with a more powerful routing-by-agreement algorithm. Specifically, the routing algorithm iteratively updates the proportion of how much a part (i.e. the distinct information learned from a specific subspace) should be assigned to a whole (i.e. the final output representation), based on the agreement between parts and wholes. Experimental results on linguistic probing tasks and machine translation tasks prove the superiority of the advanced information aggregation over the standard linear transformation.

Guided Image-to-Image Translation with Bi-Directional Feature Transformation

Abstract: We address the problem of guided image-to-image translation where we translate an input image into another while respecting the constraints provided by an external, user-provided guidance image. Various conditioning methods for leveraging the given guidance image have been explored, including input concatenation , feature concatenation, and conditional affine transformation of feature activations. All these conditioning mechanisms, however, are uni-directional, i.e., no information flow from the input image back to the guidance. To better utilize the constraints of the guidance image, we present a bi-directional feature transformation (bFT) scheme. We show that our bFT scheme outperforms other conditioning schemes and has comparable results to state-of-the-art methods on different tasks.

Low-Resource Syntactic Transfer with Unsupervised Source Reordering

Abstract: We describe a cross-lingual transfer method for dependency parsing that takes into account the problem of word order differences between source and target languages. Our model only relies on the Bible, a considerably smaller parallel data than the commonly used parallel data in transfer methods. We use the concatenation of projected trees from the Bible corpus, and the gold-standard treebanks in multiple source languages along with cross-lingual word representations. We demonstrate that reordering the source treebanks before training on them for a target language improves the accuracy of languages outside the European language family. Our experiments on 68 treebanks (38 languages) in the Universal Dependencies corpus achieve a high accuracy for all languages. Among them, our experiments on 16 treebanks of 12 non-European languages achieve an average UAS absolute improvement of 3.3% over a state-of-the-art method.

Information Aggregation for Multi-Head Attention with Routing-by-Agreement

Abstract: Multi-head attention is appealing for its ability to jointly extract different types of information from multiple representation subspaces. Concerning the information aggregation, a common practice is to use a concatenation followed by a linear transformation, which may not fully exploit the expressiveness of multi-head attention. In this work, we propose to improve the information aggregation for multi-head attention with a more powerful routing-by-agreement algorithm. Specifically, the routing algorithm iteratively updates the proportion of how much a part (i.e. the distinct information learned from a specific subspace) should be assigned to a whole (i.e. the final output representation), based on the agreement between parts and wholes. Experimental results on linguistic probing tasks and machine translation tasks prove the superiority of the advanced information aggregation over the standard linear transformation.

Computer-Implemented Method And System Of Tamper-Evident Recording Of A Plurality Of Service Data Items

Abstract: A computer-implemented method and a corresponding system of tamper-evident recording of a plurality of service data items are provided. Each service data item is associated with a data item verification fingerprint. A processing routine is conducted, in which an aggregated verification fingerprint is computed from at least a plurality of data item verification fingerprints using at least one one-way compression function, so that the aggregated verification fingerprint has a bit length, which is less than a bit length of a concatenation of the data item verification fingerprints. The aggregated verification fingerprint is then stored in at least one blockchain, so that a tamper-evident verification of each service data item is possible, while the storage of the aggregated verification fingerprint is decoupled from the service data items.

Capacity Results for the Noisy Shuffling Channel

Abstract: Motivated by DNA-based storage, we study the noisy shuffling channel, which can be seen as the concatenation of a standard noisy channel (such as the BSC) and a shuffling channel, which breaks the data block into small pieces and shuffles them. This channel models a DNA storage system, by capturing two of its key aspects: (1) the data is written onto many short DNA molecules that are stored in an unordered way and (2) the molecules are corrupted by noise at synthesis, sequencing, and during storage. For the BSC-shuffling channel we characterize the capacity exactly (for a large set of parameters), and show that a simple index-based coding scheme is optimal.

Quantitative bounds in the non-linear Roth theorem

Abstract: We show that any subset of $[N]$ of density at least $(\log\log{N})^{-2^{-157}}$ contains a nontrivial progression of the form $x,x+y,x+y^2$. This is the first quantitatively effective version of the Bergelson--Leibman polynomial Szemer\'edi theorem for a progression involving polynomials of differing degrees. In the course of the proof, we also develop a quantitative version of a special case of a concatenation theorem of Tao and Ziegler, with polynomial bounds.

A Closer Look at the Optimization Landscapes of Generative Adversarial Networks

Abstract: Generative adversarial networks have been very successful in generative modeling, however they remain relatively challenging to train compared to standard deep neural networks. In this paper, we propose new visualization techniques for the optimization landscapes of GANs that enable us to study the game vector field resulting from the concatenation of the gradient of both players. Using these visualization techniques we try to bridge the gap between theory and practice by showing empirically that the training of GANs exhibits significant rotations around Local Stable Stationary Points (LSSP), similar to the one predicted by theory on toy examples. Moreover, we provide empirical evidence that GAN training converge to a stable stationary point which is a saddle point for the generator loss, not a minimum, while still achieving excellent performance.

Conjoint measurement undone

Abstract: According to classical measurement theory, fundamental measurement necessarily requires the operation of concatenation qua physical addition. Quantities which do not allow this operation are measur...

Multi-scale Cross-path Concatenation Residual Network for Poisson denoising

Abstract: The signal degradation due to the Poisson noise is a common problem in the low-light imaging field. Recently, deep learning employing the convolution neural network for image denoising has drawn considerable attention owing to its favourable denoising performance. On the basis of the fact that the reconstruction of corrupted pixels can be facilitated by the context information in image denoising, the authors propose a deep multi-scale cross-path concatenation residual network (MC 2 RNet) which incorporates cross-path concatenation modules for Poisson denoising. Multiple paths are achieved by the cross-path concatenation operation and the skip connection. As a consequence, multi-scale context representations of images under different receptive fields can be learnt by MC 2 RNet. With the residual learning strategy, MC 2 RNet learns the residual between the noisy image and the latent clean image rather than the direct mapping to facilitate model training. Specially, unlike existing discriminative Poisson denoising algorithms that train a model only for the specific noise level, they aim to train a single model for handling Poisson noise with different levels, i.e. blind Poisson denoising. Quantitative experiments demonstrate that the proposed model is superior over the state-of-the-art Poisson denoising approaches in terms of peak signal-to-noise ratio and visual effect.

The Multispecies Coalescent Model Outperforms Concatenation across Diverse Phylogenomic Data Sets

Abstract: A statistical framework of model comparison and model validation is essential to resolving the debates over concatenation and coalescent models in phylogenomic data analysis. A set of statistical tests are here applied and developed to evaluate and compare the adequacy of substitution, concatenation, and multispecies coalescent (MSC) models across 47 phylogenomic data sets collected across tree of life. Tests for substitution models and the concatenation assumption of topologically concordant gene trees suggest that a poor fit of substitution models (44% of loci rejecting the substitution model) and concatenation models (38% of loci rejecting the hypothesis of topologically congruent gene trees) is widespread. Logistic regression shows that the proportions of GC content and informative sites are both negatively correlated with the fit of substitution models across loci. Moreover, a substantial violation of the concatenation assumption of congruent gene trees is consistently observed across 6 major groups (birds, mammals, fish, insects, reptiles, and others, including other invertebrates). In contrast, among those loci adequately described by a given substitution model, the proportion of loci rejecting the MSC model is 11%, significantly lower than those rejecting the substitution and concatenation models, and Bayesian model comparison strongly favors the MSC over concatenation across all data sets. Species tree inference suggests that loci rejecting the MSC have little effect on species tree estimation. Due to computational constraints, the Bayesian model validation and comparison analyses were conducted on the reduced data sets. A complete analysis of phylogenomic data requires the development of efficient algorithms for phylogenetic inference. Nevertheless, the concatenation assumption of congruent gene trees rarely holds for phylogenomic data with more than 10 loci. Thus, for large phylogenomic data sets, model comparison analyses are expected to consistently and more strongly favor the coalescent model over the concatenation model. Our analysis reveals the value of model validation and comparison in phylogenomic data analysis, as well as the need for further improvements of multilocus models and computational tools for phylogenetic inference.

A method to concatenate multiple short time series for evaluating dynamic behaviour during walking.

Abstract: Gait variability is a sensitive metric for assessing functional deficits in individuals with mobility impairments. To correctly represent the temporal evolution of gait kinematics, nonlinear measures require extended and uninterrupted time series. In this study, we present and validate a novel algorithm for concatenating multiple time-series in order to allow the nonlinear analysis of gait data from standard and unrestricted overground walking protocols. The full-body gait patterns of twenty healthy subjects were captured during five walking trials (at least 5 minutes) on a treadmill under different weight perturbation conditions. The collected time series were cut into multiple shorter time series of varying lengths and subsequently concatenated using a novel algorithm that identifies similar poses in successive time series in order to determine an optimal concatenation time point. After alignment of the datasets, the approach then concatenated the data to provide a smooth transition. Nonlinear measures to assess stability (Largest Lyapunov Exponent, LyE) and regularity (Sample Entropy, SE) were calculated in order to quantify the efficacy of the concatenation approach using intra-class correlation coefficients, standard error of measurement and paired effect sizes. Our results indicate overall good agreement between the full uninterrupted and the concatenated time series for LyE. However, SE was more sensitive to the proposed concatenation algorithm and might lead to false interpretation of physiological gait signals. This approach opens perspectives for analysis of dynamic stability of gait data from physiological overground walking protocols, but also the re-processing and estimation of nonlinear metrics from previously collected datasets.

Generic Results for Concatenation Hierarchies

Abstract: In the theory of formal languages, the understanding of concatenation hierarchies of regular languages is one of the most fundamental and challenging topics. In this paper, we survey progress made on this problem since 1971. We also establish new generic statements regarding this problem.

Efficient Low-Complexity Decoding of CCSDS Reed–Solomon Codes Based on Justesen’s Concatenation

Abstract: Forward error correction (FEC) is a key capability in modern satellite communications that provide the system designer with the needed flexibility to comply with the different applications' requirements. Reed-Solomon (RS) codes are well known for their ability to optimize between the system power, bandwidth, data rate, and the quality of service. This paper introduces an efficient decoding scheme for decoding the RS codes adhering to the Consultative Committee for Space Data Systems (CCSDS) standards based on Justesen's construction of concatenation. To maintain the standard output size, the proposed scheme first encodes every m - 1 bits using the single-parity-check (SPC) code, while the RS code encodes K SPC codewords into N symbols that are of the same size as CCSDS standard. Decoding on the inner SPC code is based on maximum-likelihood decoding Kaneko algorithm, while for the proposed coding scheme, the reduced test-pattern Chase algorithm is adapted for decoding the outer RS code. The simulation results show the coding gains of 1.4 and 7 dB compared with the algebraic decoding of RS codes over the AWGN and Rayleigh fading channels, respectively. Moreover, the adopted reduced test-pattern Chase algorithm for decoding the RS code achieves an overall complexity reduction of 40% compared with the conventional Chase decoding algorithm.

Constructing Two-Level Designs by Concatenation of Strength-3 Orthogonal Arrays

Abstract: Two-level orthogonal arrays of N runs, k factors, and a strength of 3 provide suitable fractional factorial designs in situations where many of the main effects are expected to be active, as well a...

Hybrid hidden Markov models and artificial neural networks for handwritten music recognition in mensural notation

Abstract: In this paper, we present a hybrid approach using hidden Markov models (HMM) and artificial neural networks to deal with the task of handwritten Music Recognition in mensural notation. Previous works have shown that the task can be addressed with Gaussian density HMMs that can be trained and used in an end-to-end manner, that is, without prior segmentation of the symbols. However, the results achieved using that approach are not sufficiently accurate to be useful in practice. In this work, we hybridize HMMs with deep multilayer perceptrons (MLPs), which lead to remarkable improvements in optical symbol modeling. Moreover, this hybrid architecture maintains important advantages of HMMs such as the ability to properly model variable-length symbol sequences through segmentation-free training, and the simplicity and robustness of combining optical models with N-gram language models, which provide statistical a priori information about regularities in musical symbol concatenation observed in the training data. The results obtained with the proposed hybrid MLP-HMM approach outperform previous works by a wide margin, achieving symbol-level error rates around 26%, as compared with about 40% reported in previous works.

Real-time Object Detection via Pruning and a Concatenated Multi-feature Assisted Region Proposal Network

Abstract: Object detection is an important research area in the field of computer vision. Its purpose is to find all objects in an image and recognize the class of each object. Since the development of deep learning, an increasing number of studies have applied deep learning in object detection and have achieved successful results. For object detection, there are two types of network architectures: one-stage and two-stage. This study is based on the widely-used two-stage architecture, called Faster R-CNN, and our goal is to improve the inference time to achieve real-time speed without losing accuracy.First, we use pruning to reduce the number of parameters and the amount of computation, which is expected to reduce accuracy as a result. Therefore, we propose a multi-feature assisted region proposal network composed of assisted multi-feature concatenation and a reduced region proposal network to improve accuracy. Assisted multi-feature concatenation combines feature maps from different convolutional layers as inputs for a reduced region proposal network. With our proposed method, the network can find regions of interest (ROIs) more accurately. Thus, it compensates for loss of accuracy due to pruning. Finally, we use ZF-Net and VGG16 as backbones, and test the network on the PASCAL VOC 2007 dataset.

On the Expressive Power of GF(2)-Grammars

Abstract: GF(2)-grammars, recently introduced by Bakinova et al. (“Formal languages over GF(2)”, LATA 2018), are a variant of ordinary context-free grammars, in which the disjunction is replaced by exclusive OR, whereas the classical concatenation is replaced by a new operation called GF(2)-concatenation: \(K \odot L\) is the set of all strings with an odd number of partitions into a concatenation of a string in K and a string in L. This paper establishes several results on the family of languages defined by these grammars. Over the unary alphabet, GF(2)-grammars define exactly the 2-automatic sets. No language of the form \(\{a^n b^{f(n)} \,\mid \, n \geqslant 1\}\), with uniformly superlinear f, can be described by any GF(2)-grammar. The family is not closed under union, intersection, classical concatenation and Kleene star, non-erasing homomorphisms. On the other hand, this family is closed under injective nondeterministic finite transductions, and contains a hardest language under reductions by homomorphisms.

A non-linear channel code for covert communications

Abstract: This paper presents an explicit channel code design for covert communications in the Binary Symmetric Channel. The proposed architecture is composed of the serial concatenation of a linear code and a graph-based non-linear code baptized as moderate-density non-linear code. This non-linear code encompasses pulse position modulation as a particular case. In order to guarantee covertness, a scrambling sequence that is not known to the warden is employed.