Single-track circuit codes

By the problem, called a representation of the integers, is meant the encoding of the positive integers without a known upper bound, for which unique decoding can be provided. From the viewpoint of information theory, this problem has been discussed theoretically in its relation to the universality, asymptotic optimality, and computation theory. The result in those approaches has been applied to the data compression scheme for the type of data referring to the past as well as the URR and other floating-pointnumber representations with variable exponential length. This paper discusses representation of the integers problem from the viewpoint of the codeword-length function, which is the function to represent the length of the codeword. As a result, a general construction method is presented which has the desirable property and can uniquely encode all representations. Several methods are given from this approach, which can construct not only the traditional representations of the integers but also the first representations of the integers which has not been considered. It is noted first that two construction methods of codeword length, which are independent of the encoding, are considered. One is based on the combination of the codeword-length functions, and the other is based on the codeword-length distribution. More precisely, it is shown that not only are the traditional representations derived, but also the representations that have not been considered in the past. Using detailed examples, it is shown that the computational complexity of the encoding and decoding depends on the codeword-length function.

In this article the triangular codes found dependence of the power of these codes on the length of codewords in them.The methods of construction codes and some triangular propose an effective general method for constructing such codes based on monotone Boolean functions.Designed with correcting codes cryptosystem on the basis of such a code, which allows one to correct the error.The advantage of this cryptosystem is the speed of coding and decoding, and the ability to quickly change the code without changing tables, coding and decoding.Change the code is implemented using the substitution, and the choice of codes is very large.The number of possible codes is 20! (approximately equal to 2.4*10 18 ) has at length codeword of 20.

Due to the fact that we lack a general construction method of (N, w, λ, λ) multiple-length (ML) optical orthogonal codes (OOCs), a general construction method with high efficiency for ML OOCs with arbitrary cross-correlation λ is presented. The main idea of the method is to construct a variable-length mapping sequence with unparallel λ positions, with which to map short-length OOCs into long-length OOCs to realize the general construction of ML OOCs with correlation value λ with high efficiency by the Johnson bound. The cardinality of multiple-length mapping sequences is derived. Based on the cardinality, the fundamentals of constructing the aforementioned multiple-length mapping sequences are presented and proved. The construction method of ML OOCs with arbitrary cross-correlation λ is given. Simulation results show that the method can construct ML OOCs with arbitrary λ the applications of ML OOCs show that the method is practical for constructing ML OOCs to support multiple service.

A reconfigurable cyclic shifter is a key element of a QC-LDPC decoder, which is crucial for 5G communication systems. If a traditional reconfigurable cyclic shifter can only shift one input of variable size at a time, a traditional QC-LDPC decoder can only decode one codeword at a time as well. Part of the circuitry of the traditional QC-LDPC decoder inevitably stays in idle during the decoding process if the length (or the lifting parameter) of a codeword is not the maximum, resulting in low hardware efficiency. A segmented reconfigurable cyclic shifter is proposed in this paper, which can be divided into multiple segments of different sizes. Each segment can perform a cyclic shift of an input of different sizes and of different shift values independently. Furthermore, a methodology is proposed to upgrade any state-of-the-art QC-LDPC decoder to a segmented QC-LDPC decoder, by using the proposed segmented shifter. The upgraded segmented QC-LDPC decoder is able to parallelly decode multiple codewords (or inputs) of different lengths at a time. A test chip of the proposed segmented QC-LDPC decoder with the proposed segmented reconfigurable cyclic shifter has been fabricated in a 0.18-<inline-formula> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> CMOS technology to demonstrate the feature of parallelly decoding multiple codewords. The performance analysis shows that when the number of small codewords is increased from 0 to 100000 per second, the throughput of the traditional QC-LDPC decoder drops from 844.80 Mbps to 4.40 Mbps, while the QC-LDPC decoder with the proposed segmented shifter only slightly drops to 814.01 Mbps. By applying the segmented QC-LDPC decoder in 5G base stations, the base stations are enabled to support more low-traffic users.

Since the logical structure of a data base can be represented by a tree or graph, it is quite natural for us to view the process of designing a data base as that of constructing a tree or a graph. A general method for constructing such a tree or graph is provided. There are three important elements in this general construction method; namely, a set of binary relations, an algorithm for constructing subsets of a set, and an algorithm for selecting an element from the given set of objects. The use of different relations and algorithms results in different information structures, as list, tree, ring, etc. Thus the problem of information organization and storage is reduced to that of defining relations and formulating algorithms under a given set of constraints. The results presented may be valuable to designers as useful design concepts, and may serve as a basis for developing a formal theory on the subject.

Observing the threshold effect of CDMA systems, this paper proposes a simple, fair protocol suitable for the CDMA environment, which does not need the additional feedback channel but can still achieve the goal of error control. Based on the same rationale as the CSMA/CD protocol, this protocol is designed to avoid collision or congestion of traffic before formal transmission of a packet. By the handshake procedure, the intended transmitter is able to test the channel quality and the receiver's status using a very short handshake packet. Therefore, channel traffic can be controlled to avoid overload. The throughput and reliability are analyzed based on the underlying Markovian models. Numerical results are compared to other error control schemes and show that with a reasonably short handshake time compared to the packet transmission time, this handshake protocol with simple forward error correction offers an excellent alternative for error control and can even improve the throughput performance.

This chapter covers averages defined on product lattices, in particular in the intuitionistic fuzzy sets and interval-valued fuzzy sets setting. Some general construction methods and special cases are outlined. The medians on lattices are discussed in detail and several alternative forms of the median function are presented.

In this paper we discuss (left) near-rings satisfying the identities:abcd=acbd,abc=bac, orabc=acb, called medial, left permutable, right permutable near-rings, respectively. The structure of these near-rings is investigated in terms of the additive and Lie commutators and the set of nilpotent elementsN (R). For right permutable and d.g. medial near-rings we obtain a “Binomial Theorem,” show thatN (R) is an ideal, and characterize the simple and subdirectly irreducible near-rings. “Natural” examples from analysis and geometry are produced via a general construction method.

Triangular norms. Position paper II: general constructions and parameterized families

A general algebraic method for decoding all types of binary cyclic codes is presented. It is shown that such a method can correct t=[(d-1)/2] errors, where d is the true minimum distance of the given cyclic code. The key idea behind this decoding technique is a systematic application of the algorithmic procedures of Grobner bases to obtain the error-locator polynomial L(z). The discussion begins from a set of syndrome polynomials F and the ideal T(F) generated by F. It is proved here that the process of transforming F to the normalized reduced Grobner basis of I(F) with respect to the purely lexicographical ordering automatically converges to L(z). Furthermore, it is shown that L(z) can be derived from any normalized Grobner basis of I(F) with respect to any admissible total ordering. To illustrate this new approach, the procedures for decoding certain BCH codes and quadratic residue codes are demonstrated. >

Synthesis of Ag–Fe 3O 4 heterodimeric nanoparticles

5.6 Oxidation: C–N Bond Formation by Oxidation (Aziridines)

In this paper, a general Gray code quantized method of binary feature descriptors is proposed for fast and efficient keypoint matching on 3D point clouds. In our method, it includes 2 variable L and N. L is rule variable which can be used to set the encoding group length according to the feature of the real-valued descriptor, and N is bits variable which can be used to set the number of Gray code bits according to the actual system requirements. Be different from the exist method, such as B-SHOT, our proposed method has the advantages of reasonable and flexible. As an example, our method is applied on the feature descriptor SHOT and tested in a standard benchmark dataset, different variable combinations of L and N are tested in the Gray code quantized processes, the best combination of L and N is dubbed as GRAY-SHOT through performance comparison. At last, GRAY-SHOT is compared with the state-of-the-art binary 3D feature descriptor B-SHOT, experimental evaluation result shows that GRAY-SHOT offers better keypoint matching performances to B-SHOT on a standard benchmark dataset with a slight more memory footprint and time consumption.

A new class of codes for frame synchronization is proposed. Commonly, the beginning of every fixed or variable-length frame is identified by a given contiguous sequence called a prefix. To avoid the occurrence of the prefix elsewhere in the frame, a prefix synchronizable code (PS-code) is used. PS-codes have the property that the prefix does not occur in any codeword or in any concatenation of codewords in any position other than the first position. The new codes, termed partial-prefix synchronizable codes (PPS-codes), use a fixed sequence of symbols that is interspersed with symbols that carry information. The contiguous sequence from the first fixed symbol to the last fixed symbol is called a partial-prefix. Consequently, not one but a set of possible prefixes is used, and none of these prefixes is allowed to occur at any other than the first position of a codeword. The cardinality of PPS-codes is determined, and coding algorithms are proposed which have a computational complexity proportional to the length of the codewords. It is demonstrated that in comparison with PS-codes, PPS-codes have similar coding and prefix detection complexity, but they have a larger code size and have better error control capabilities.

Urban waterlogging is a typical complex disaster in the process of modern urbanization, triggered by the superimposition of multiple structural contradictions. To enhance the accuracy and timeliness of water accumulation depth prediction and provide core technical support for the full-chain prevention and control of urban waterlogging monitoring - early warning - dispatching, this paper proposes the DE-Transformer-BiLSTM regression algorithm. The research first conducted a correlation analysis and then tested and verified it through multiple machine learning algorithms. The results showed that the algorithm performed the best on all core regression indicators: Compared with traditional integrated models such as ExtraTrees and Random Forest, its MSE is reduced by 43.7%, RMSE is reduced by 25.0%, MAE is reduced by 23.4%, MAPE is reduced by 11.9%, and R is increased to 0.988, significantly optimizing error control and data interpretation capabilities. Compared with other deep learning models such as SAIS-CNN-BILSTM and NRBO-Transformer-BiLSTM, with better hyperparameter optimization effects and stronger long-range dependency and bidirectional temporal feature modeling capabilities, it leads by 37.4% to 51.9% in indicators such as MSE and RMSE, and maintains the lowest MAPE. Compared with the second-tier models such as Decision Tree and CatBoost, and the third-tier models such as KNN, the advantages are more significant. The MSE is only 26.6% of CatBoost and 1.5% of KNN, and the R is close to the theoretical maximum value of 1. The advantage of this algorithm stems from its unique architecture. The DE algorithm efficiently optimizes hyperparameters to reduce labor costs, the Transformer captures long-range features, and BiLSTM extracts bidirectional temporal information. The combination of the three not only solves the problem of difficult adjustment of hyperparameters in deep learning models but also makes up for the deficiency of complex feature modeling in traditional models. It provides a reliable technical solution for the precise prevention and control of urban flooding.