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Data pre-processing is the first step of using SCADA data to study the performance of wind turbines. However, there is a lack of knowledge of how to obtain more effective data pre-processing algorithms. This paper fully explores multiple data pre-processing algorithms for power curve modeling. A three-stage data processing mode is proposed, namely, preliminary data filtering and compensation (Stage I), secondary data filtering (Stage II), and single-valued processing (Stage Ⅲ). Different data processing algorithms are selected at different stages and are finally merged into nine data processing algorithms. A novel evaluation method based on energy characteristic consistency (ECC) is proposed to evaluate the reliability of various algorithms. The influence of sliding mode and benchmark of Binning on data processing has been fully investigated through indicators. Four wind turbines are selected to verify the advantages and disadvantages of the nine data processing methods. The result shows that at the same wind speed, the rotational speed and power values obtained by MLE (maximum likelihood estimation) are relatively high among the three single-valued methods. Among the three outlier filtering methods, the power value obtained by KDE (kernel density estimation) is relatively large. In general, KDE-LSM (least square method) has good performance in general. The sum of four evaluating index values obtained by KDE-LSM from four wind turbines is the smallest. [ABSTRACT FROM AUTHOR]

This paper proposes an exact algorithm to solve the one-to-one multiobjective shortest path problem. The solution involves determining a set of nondominated paths between two given nodes in a graph that minimizes several objective functions. This study is motivated by the application of this solution method to determine cycling itineraries. The proposed algorithm improves upon a label-correcting algorithm to rapidly solve the problem on large graphs (i.e., up to millions of nodes and edges). To verify the performance of the proposed algorithm, we use computational experiments to compare it with the best-known methods in the literature. The numerical results confirm the efficiency of the proposed algorithm. Summary of Contribution: The paper deals with a classic operations research problem (the one-to-one multiobjective shortest path problem) and is motivated by a real application for cycling itineraries. An efficient method is proposed and is based on a label-correcting algorithm into which several additional improvement techniques are integrated. Computational experiments compare this algorithm with the best-known methods in the literature to validate the performance on large-size graphs (Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) instances from the ninth DIMACS challenge). New instances from the context of cycling itineraries are also proposed. [ABSTRACT FROM AUTHOR]

Galois hulls are generalizations of Euclidean and Hermitian hulls, which have attracted interest because of their important applications in determining the complexity of some algorithms about linear codes and in constructing entanglement-assisted quantum error-correcting codes (EAQECCs). In this paper, the whole contribution is two-folded. On one hand, we propose explicit methods to construct linear codes of larger lengths with Galois hulls of arbitrary dimensions from given Galois self-orthogonal codes. Conditions required in our approach are proven to be relatively weak. On the other hand, we apply these results to construct EAQECCs. Two bounds for EAQECCs constructed from linear codes with prescribed dimensional Galois hull are given and EAQECCs with rates greater than or equal to 1 2 and positive net rates can be obtained. We also present many interesting examples to explain visually how these two aspects work. [ABSTRACT FROM AUTHOR]

Error-Correcting Output Codes has become a well-known, established technique for multiclass classification due to its simplicity and efficiency. Each binary split contains different original classes. A noncompetent classifier emerges when it classifies an instance whose real class does not belong to the metasubclasses which is used to learn the classifier. How to reduce the error caused by the noncompetent classifiers under diversity big enough is urgent for ECOC classification. The weighted decoding strategy can be used to reduce the error caused by the noncompetence contradiction through relearning the weight coefficient matrix. To this end, a new weighted decoding strategy taking the classifier competence reliability into consideration is presented in this paper, which is suitable for any coding matrix. Support Vector Data Description is applied to compute the distance from an instance to the metasubclasses. The distance reflects the competence reliability and is fused as the weight in the base classifier combination. In so doing, the effect of the competent classifiers on classification is reinforced, while the bias induced by the noncompetent ones is decreased. Reflecting the competence reliability, the weights of classifiers for each instance change dynamically, which accords with the classification practice. The statistical simulations based on benchmark datasets indicate that our proposed algorithm outperforms other methods and provides new thought for solving the noncompetence problem. [ABSTRACT FROM AUTHOR]

In this paper we consider the problem of encoding data into repeat-free sequences in which sequences are imposed to contain any k-tuple at most once (for predefined k). First, the capacity of the repeat-free constraint are calculated. Then, an efficient algorithm, which uses two bits of redundancy, is presented to encode length-n sequences for k = 2 + 2 log (n). This algorithm is then improved to support any value of k of the form k = a log (n), for 1 < a, while its redundancy is o(n). We also calculate the capacity of repeat-free sequences when combined with local constraints which are given by a constrained system, and the capacity of multi-dimensional repeat-free codes. [ABSTRACT FROM AUTHOR]

• The first attempt to design a GEP-based codematrix generation algorithm. The individual structure of GEP allows the codematrix to be optimized in a much faster and more effective way. • The feature selection scheme is combined with the design of codematrix, to accomplish the feature selection and codematrix optimization simultaneously. • A greedy strategy-based adaptive optimization method to further improve the individual's quality to deal with hard classes by appending proper columns to the codematrix. The multi-class classification task is one of the most common tasks in machine learning. As a typical solution based on a partitioning strategy, Error-Correcting Output Codes (ECOC) can transform a multi-class classification problem into multiple binary classification problems. The key of ECOC is to construct an effective codematrix to represent a set of class decomposition schemes, which transforms a multiclass problem into a group of binary class problems. Consequently, the design of a fast and effective ECOC codematrix generation method is of great research significance and value for solving multi-class classification problems. In ECOC algorithms, the design of codematrix is treated as a combination problem between different code columns, in which the evolutionary algorithm shows a great advantage. Based on this consideration, the Gene Expression Programming (GEP) is applied to search for the codematrix with high performance because its expressive tree structure makes it well represent codematrcies for subsequent optimization operations. This paper proposes an adaptive ECOC algorithm based on Gene Expression Programming (GEP) and similarity measurement matrix, named GEP-ECOC. In our GEP, each individual represents a set of columns to form a random ECOC codematrix, which is optimized in the evolutionary process. Meanwhile, the crossover and mutation operations are modified to include a legality checking process to ensure that the generated codematrix satisfies the ECOC constraints. The GEP-based ECOC codematrix generation algorithm can quickly produce a codematrix with better performance, which ensures the efficiency of the algorithm to a certain extent. In addition, an adaptive algorithm based on a similarity measurement matrix is proposed to add new columns to the current codematrix, aiming to better handle hard classes. Our algorithm is compared with other algorithms on various data sets, and the experimental results confirm that our GEP-ECOC can balance the efficiency and performance of the algorithm and achieve higher performance. [ABSTRACT FROM AUTHOR]

Hamming codes are of primary concern in information theory and its applications. Despite a number of researches that have been conducted on such codes and their characterizations, dealing with the properties of previously introduced codes in a BCK-algebraic framework has not been considered in earlier works. This paper investigates a code constructed based on BCK-algebraic models and proposes an algorithm corresponding to the presented code. It is noticeable that the suggested rendered algorithm is also established on the basis of the elements of a BCK-algebra. In fact, both the Hamming distance and dimension, associated with the presented code, can be estimated through a BCK-algebra structure due to the mechanism of its algorithm which is heavily dependent on the parity check matrix. In addition, the way in which the codes are designed contributes substantially to classification of them and to extract greater number of their attributes compared to the previous works. The highlight of the proposed method is that the number of atoms of the BCK-algebra plays a key role in calculation of the Hamming distance and dimension of these codes. Moreover, the obtained codes possess specified and recognizable Hamming distance which are essential in performing error-correcting, error-detecting and decoding tasks. [ABSTRACT FROM AUTHOR]

The performance of low-density parity-check (LDPC) codes at high signal-to-noise ratios (SNRs) is known to be limited by the presence of certain sub-graphs that exist in the Tanner graph representation of the code, for example trapping sets and absorbing sets. This paper derives a lower bound on the frame error rate (FER) of any LDPC code containing a given problematic sub-graph, assuming a particular message passing decoder and decoder quantization. A crucial aspect of the lower bound is that it is code-independent, in the sense that it can be derived based only on a problematic sub-graph and then applied to any code containing it. Due to the complexity of evaluating the exact bound, assumptions are proposed to approximate it, from which we can estimate decoder performance. Simulated results obtained for both the quantized sum-product algorithm (SPA) and the quantized min-sum algorithm (MSA) are shown to be consistent with the approximate bound and the corresponding performance estimates. Different classes of LDPC codes, including both structured and randomly constructed codes, are used to demonstrate the robustness of the approach. [ABSTRACT FROM AUTHOR]

Several 100 Gbps Ethernet standards for backplane, copper cables and fiber optic that include forward error correction based on Reed-Solomon (RS) codes have been recently approved, being an important issue not only to achieve high data rates but also to keep a low latency. This paper presents two low-latency and high-throughput RS decoders suitable for those standards. We propose the use of a modified Enhanced Parallel iBM Algorithm as the key equation solver (KES) stage and a novel architecture for the error evaluation block, which is suited for this KES. Implementation results are given for the RS(528,514) and RS(544,514) codes over GF(210) that reach 100 Gbps when implemented in a 90 nm CMOS process. [ABSTRACT FROM AUTHOR]

Additional check bits, which are commonly attached to the message’s input data, are normally used to minimize the error during data transmission. The receiver system implements a checking algorithm to determine if an error was occurred in the received data. This algorithm will correct a corrupted bit and recover the original message. An enhanced error detection correction code was presented to better detect and correct the corrupted conveyed bits. It improves the existing limitations of utilizing cyclic redundancy checking (CRC), Hamming code, and other checksum techniques. Also, it reduced the length of the redundancy bits which exists in CRC, the overhead of interspersing of the redundancy bits in a typical Hamming code, and the system resources such as processor time and bandwidth in checksum techniques. This paper was synthesized and simulated using the Xilinx Spartan 6 (XC7Z020-2CLG4841) FPGA. Results show that the resource utilization of the designed memory architecture using EEDC is lower compared to CRC, Hamming, and Checksum algorithms. [ABSTRACT FROM AUTHOR]

We introduce an algorithm for the generation of complement-free sets of binary m-tuples, where m is even. We also provide an implementation for this algorithm for m = 12. Such complement-free sets are needed for the generation of a new class of error-correcting codes, which were introduced by Hannusch and Lakatos. These codes build the fundamental improvement in the cryptographic system of Dömösi, Hannusch and Horváth. Therefore the generation of complement-free sets will be important for cryptographic applications. In the end of the paper we give some interesting facts about complement-free sets as combinatorial objects. [ABSTRACT FROM AUTHOR]

1 A new ECOC encoding algorithm is proposed, which separates classes into two groups by maximizing the ratio of the inter-group distance to intra-group distance. 2 A novel Soft-Coded (SC) ECOC algorithm is proposed by softening the codewords of the ECOC codematrix by considering the subordination degree of each class to both groups. 3 A new measure coverage is designed to evaluate the subordination degrees of different classes to the positive and the negative groups, and the values are set as the elements of the codematrix. 4 A self-adaptive strategy is designed to adjust codewords, making them better fit the associated learners. Error-Correcting Output Codes (ECOC) algorithms enable multiclass classification by reassigning multiple classes to the positive/negative group with the class reassignment schemes being recorded as binary/ternary hard-coded (HC) codematrices. Different classes tend to get diverse subordination degrees to the positive/negative group, providing clues to correct potential errors. However, the HC codematrices are unable to provide the information in the subordination degrees. In this paper, a Soft-Coded ECOC (SC-ECOC) scheme, namely, the Sequential Forward Floating Selection algorithm, is proposed by filling codematrices with real values instead of hard codes to improve classification performance. This algorithm divides multiple classes into two groups by maximizing the ratio of inter-group distance to intra-group distance. Then a new measure coverage is designed to evaluate the subordination degrees of different classes to both groups, which are set as the elements to form a codematrix. Furthermore, a self-adaptive strategy adjusts the value of each element to fit learners better. Experiments are carried out to verify the performance of our algorithm on various data sets, and results confirm that our algorithm can achieve more balanced results compared with the traditional HC ECOC algorithms. Besides, the values of soft codes correlate with the difficulty level of various classes to improve the multiclass classification ability. [ABSTRACT FROM AUTHOR]

Symbol-pair read channels, in which the outputs of the read process are pairs of consecutive symbols, were recently studied by Cassuto and Blaum. This new paradigm is motivated by the limitations of the reading process in high density data storage systems. They studied error correction in this new paradigm, specifically, the relationship between the minimum Hamming distance of an error correcting code and the minimum pair distance, which is the minimum Hamming distance between symbol-pair vectors derived from codewords of the code. It was proved that for a linear cyclic code with minimum Hamming distance dH , the corresponding minimum pair distance is at least dH+3 . In this paper, we show that, for a given linear cyclic code with a minimum Hamming distance dH , the minimum pair distance is at least dH +\left \lceil{ {dH/{2}}}\right \rceil . We then describe a decoding algorithm, based upon a bounded distance decoder for the cyclic code, whose symbol-pair error correcting capabilities reflect the larger minimum pair distance. Finally, we consider the case where the read channel output is a larger number, $b \geqslant 3$ , of consecutive symbols, and we provide extensions of several concepts, results, and code constructions to this setting. [ABSTRACT FROM AUTHOR]

• Maximum-Likelihood detection for soft-output in MIMO-GSM systems leads a high computational cost. • Three different algorithms that achieve Maximum-Likelihood performance are proposed to provide a reasonable computational cost in order to make a performance benchmark available. • The algorithms show reduced complexity compared to other ML algorithms, especially when the system size increases. Generalized Spatial Modulation (GSM) is a recent Multiple-Input Multiple-Output (MIMO) scheme, which achieves high spectral and energy efficiencies. Specifically, soft-output detectors have a key role in achieving the highest coding gain when an error-correcting code (ECC) is used. Nowadays, soft-output Maximum Likelihood (ML) detection in MIMO-GSM systems leads to a computational complexity that is unfeasible for real applications; however, it is important to develop low-complexity decoding algorithms that provide a reasonable computational simulation time in order to make a performance benchmark available in MIMO-GSM systems. This paper presents three algorithms that achieve ML performance. In the first algorithm, different strategies are implemented, such as a preprocessing sorting step in order to avoid an exhaustive search. In addition, clipping of the extrinsic log-likelihood ratios (LLRs) can be incorporating to this algorithm to give a lower cost version. The other two proposed algorithms can only be used with clipping and the results show a significant saving in computational cost. Furthermore clipping allows a wide-trade-off between performance and complexity by only adjusting the clipping parameter. [ABSTRACT FROM AUTHOR]

In many classification problems, neighbor data labels have inherent sequential relationships. Sequential learning algorithms take benefit of these relationships in order to improve generalization. In this paper, we revise the multi-scale sequential learning approach (MSSL) for applying it in the multi-class case (MMSSL). We introduce the error-correcting output codesframework in the MSSL classifiers and propose a formulation for calculating confidence maps from the margins of the base classifiers. In addition, we propose a MMSSL compression approach which reduces the number of features in the extended data set without a loss in performance. The proposed methods are tested on several databases, showing significant performance improvement compared to classical approaches. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new feature descriptor for images that is based on the dihedral group D 4 , the symmetry group of the square. The group action of the D 4 elements on a square image region is used to create a vector space that forms the basis for the feature vector. For the evaluation, we employed the Error-Correcting Output Coding (ECOC) algorithm and tested our model with four diverse datasets. The results from the four databases used in this paper indicate that the feature vectors obtained from our proposed D 4 algorithm are comparable in performance to that of Histograms of Oriented Gradients (HOG) model. Furthermore, as the D 4 model encapsulates a complete set of orientations pertaining to the D 4 group, it enables its generalization to a wide range of image classification applications. [ABSTRACT FROM AUTHOR]

In this paper, the most efficient (from data compaction point of view) and current image lossless coding method is presented. Being computationally complex, the algorithm is still more time efficient than its main competitors. The presented cascaded method is based on the Weighted Least Square (WLS) technique, with many improvements introduced, e.g., its main stage is followed by a two-step NLMS predictor ended with Context-Dependent Constant Component Removing. The prediction error is coded by a highly efficient binary context arithmetic coder. The performance of the new algorithm is compared to that of other coders for a set of widely used benchmark images. [ABSTRACT FROM AUTHOR]