Triangular Code Research Articles

Triangle codes and tracer lights based absolute positioning method for terminal visual docking of autonomous underwater vehicles

PurposeDocking technology plays a crucial role in enabling long-duration operations of autonomous underwater vehicles (AUVs). Visual positioning solutions alone are susceptible to abnormal drift values due to the challenging underwater optical imaging environment. When an AUV approaches the docking station, the absolute positioning method fails if the AUV captures an insufficient number of tracers. This study aims to to provide a more stable absolute position visual positioning method for underwater terminal visual docking.Design/methodology/approachThis paper presents a six-degree-of-freedom positioning method for AUV terminal visual docking, which uses lights and triangle codes. The authors use an extended Kalman filter to fuse the visual calculation results with inertial measurement unit data. Moreover, this paper proposes a triangle code recognition and positioning algorithm.FindingsThe authors conducted a simulation experiment to compare the underwater positioning performance of triangle codes, AprilTag and Aruco. The results demonstrate that the implemented triangular code reduces the running time by over 70% compared to the other two codes, and also exhibits a longer recognition distance in turbid environments. Subsequent experiments were carried out in Qingjiang Lake, Hubei Province, China, which further confirmed the effectiveness of the proposed positioning algorithm.Originality/valueThis fusion approach effectively mitigates abnormal drift errors stemming from visual positioning and cumulative errors resulting from inertial navigation. The authors also propose a triangle code recognition and positioning algorithm as a supplementary approach to overcome the limitations of tracer light positioning beacons.

Triangular code: Near-optimal linear time fountain code

In this paper, we propose Triangular Code (TC), a new class of fountain code with near-zero redundancy and linear encoding and decoding computational complexities of O(Lklogk), where k is the packet batch size and L is the packet data length. Different from previous works where the optimal performance of codes has been shown under asymptotic assumption, TC enjoys near-zero redundancy even under non-asymptotic settings for small-moderate number of packets. These features make TC suitable for practical implementation in battery-constrained devices in IoT, D2D and M2M network paradigms to achieve scalable reliability, and minimize latency due to its low decoding delay. TC is a non-linear code, which is encoded using the simple shift and XOR addition operations, and decoded using the simple back-substitution algorithm. Although it is nonlinear code at the packet level, it remains linear code when atomized at the bit level. We use this property to show that the back-substitution decoder of TC is equivalent to the Belief Propagation (BP) decoder of LT code. Therefore, TC can benefit from rich prolific literature published on LT code, to design efficient code for various applications. Despite the equivalency between the decoders of TC and LT code, we show that compared to state-of-the-art optimized LT code, TC reduces the redundancy of LT code by 68%–99% for k reaching 1024.© 2022 Published by Elsevier Ltd.

Sliding-Window-Based RNC Scheme in UAV Multicasting: Performance Analysis and Network Optimization

Unmanned aerial vehicles (UAVs)-enabled multicasting network has attracted significant attention in recent years. However, there are still some disadvantages of existing multicasting schemes used in these systems, such as low transmission efficiency and high feedback overhead. Accordingly, we propose a sliding coding window (SCW)-based random network coding (SCWRNC) scheme for a UAV multicasting network where one UAV base station is dispatched to the multicast data stream to multiple user equipments (UEs). The proposed scheme includes an SCW scheduling original packets for encoding, a lower triangular coding structure enabling UEs to decode out information even without receiving a full set of coded packets, and a feedback-compete mechanism requiring only one UE to send feedback information. The packet scheduling process is described as a five-tuple Markov decision process. Then, we give a theoretical analysis of the proposed scheme, based on which the sliding steps of SCW and the UAV hovering location are jointly optimized to maximize the system throughput. The optimal sliding steps are obtained by applying the Greedy scheduling technique, while the UAV optimal position is obtained by minimizing the maximum outage probability of all UEs. Furthermore, we also propose a flexible feedback mechanism, which enables more than one UE to send feedback for systems with sufficient resources and a “F-SCWRNC” scheme for systems where no UE is allowed to send feedback. Numerical results show that both the proposed SCWRNC scheme and F-SCWRNC scheme could achieve significant throughput gain over the existing ones.

Construction of Polygonal Color Codes from Hyperbolic Tesselations

This current work propose a technique to generate polygonal color codes in the hyperbolic geometry environment. The color codes were introduced by Bombin and Martin-Delgado in 2007, and the called triangular color codes have a higher degree of interest because they allow the implementation of the Clifford group, but they encode only one qubit. In 2018 Soares e Silva extended the triangular codes to the polygonal codes, which encode more qubits. Using an approach through hyperbolic tessellations we show that it is possible to generate Hyperbolic Polygonal codes, which encode more than one qubit with the capacity to implement the entire Clifford group and also having a better coding rate than the previously mentioned codes, for the color codes on surfaces with boundary with minimum distance d = 3.

Resource Tuned Optimal Random Network Coding for Single Hop Multicast future 5G Networks

Optimal random network coding is reduced complexity in computation of coding coefficients, computation of encoded packets and coefficients are such that minimal transmission bandwidth is enough to transmit coding coefficient to the destinations and decoding process can be carried out as soon as encoded packets are started being received at the destination and decoding process has lower computational complexity. But in traditional random network coding, decoding process is possible only after receiving all encoded packets at receiving nodes. Optimal random network coding also reduces the cost of computation. In this research work, coding coefficient matrix size is determined by the size of layers which defines the number of symbols or packets being involved in coding process. Coding coefficient matrix elements are defined such that it has minimal operations of addition and multiplication during coding and decoding process reducing computational complexity by introducing sparseness in coding coefficients and partial decoding is also possible with the given coding coefficient matrix with systematic sparseness in coding coefficients resulting lower triangular coding coefficients matrix. For the optimal utility of computational resources, depending upon the computational resources unoccupied such as memory available resources budget tuned windowing size is used to define the size of the coefficient matrix.

A two-dimensional triangular medical coding system for storing and reporting medical information

Medical coding is an integral part of modern communication standards that help transform many types of clinical information such as patient information. The need to implement a standardized and a universal medical coding system is essential. The current study introduces a unique two-dimensional triangular medical coding system to identify, store and transmit clinical data based on the ICD-10 system between health institutions. The coding system comprises a triangular coding unit that can be arranged in six different standard geometric shapes representing the coding mechanism. A specific number of coding units are arranged in columns to form a cryptographic matrix. The matrix is comprised of many coding zones each generating a total number of “36” possible variations. The cryptographic code is then recognized by a digital scanner that is able to identify each triangular coding unit using a hypothetical signal triangle. The current coding system provides a simple process to store private medical information including patient ’ s name, age, address, and medical history. This information can be then transferred electronically or printed without the fear of privacy or security violations.

Modeling Three-Dimensional Geometric Shapes from Nucleic Acid Sequences Using a Computerized Numerical Control

The nucleic acid sequence is an astonishing and a complicated coding system that is capable of producing a complete human body with of its molecules, cells, tissue and organs. Nucleic acid has been used in many fields of sciences for the preservation and encoding of different types of information. The current project describes the use of a computerized numerical control device to form 3D geometric shapes from nucleic acid sequences. The device employs dynamic algorithms to store and then identify the strings of letters of the nucleic acid sequence, transforming them into trigonometric matrices of continues triangular codes and ultimately translating each one of matrix codes into points in 3D space to construct three-dimensional geometric shapes. This method is useful for storing architectural design and blueprints, as well as, helping to establish a standardized coding technology for 3D printing devices.

Construction of color codes from polygons

We propose a procedure for constructing new classes of codes, called polygonal color codes. This technique expands the triangular color codes introduced by Bombin and Martin-Delgado in 2007. Triangular color codes, built on a two-dimensional Euclidean surface with three edges, implement the entire Clifford group, but they only encode one qubit. In our case, polygonal color codes are constructed on two-dimensional surfaces with n edges, with n ≥ 3 , increasing the number of encoded qubits. Considering a surface with boundary and evaluating the generators of the first homology group of this surface, we may increase the dimension of the code without losing the transversal implementation of the Clifford group. In addition, we construct two codes, one with 2 and one with 3 encoded qubits, which exemplify the method and show that we can generate codes with better parameters than the known triangular codes. For one of these constructions, we also give general parameters.

Construction of Cryptosystem on the Basis of Triangular Codes

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.

PARALLEL IMPLEMENTATION OF DOMAIN DECOMPOSITION BASED IMAGE COMPRESSION ALGORITHM

AbstractThis paper presents algorithms for parallel implementation of the recently reported binary tree triangular coding (BTTC ) method for lossy image compression. We present parallel BTTC algorithms for four models: (1) parallel random access machine (PRAM), (2) hypercube, (3) 2-D mesh, and (4) sparse mesh, with their respective time complexities as O((n/p) log(n/p)), O((n/p) (log(n/p) +log p)), O((n/p) (log(n/p)+log p)), and O((n/p) (log(n/p)+log p)) for encoding and θ(n/p), θ ((n/p) (1+log p)), θ((n/p) (1+log p)), and θ((n/p) (1+log p)) for decoding, wheren is total number of pixels in the image and p is number of processors.

Parallel Implementation of Domain Decomposition Based Image Compression Algorithm

This paper presents algorithms for parallel implementation of the recently reported binary tree triangular coding (BTTC ) method for lossy image compression. We present parallel BTTC algorithms for four models: (1) parallel random access machine (PRAM), (2) hypercube, (3) 2-D mesh, and (4) sparse mesh, with their respective time complexities as O((n/p) log(n/p)), O((n/p) (log(n/p) +log p)), O((n/p) (log(n/p)+log p)), and O((n/p) (log(n/p)+log p)) for encoding and θ(n/p), θ ((n/p) (1+log p)), θ((n/p) (1+log p)), and θ((n/p) (1+log p)) for decoding, wheren is total number of pixels in the image and p is number of processors.

Space partitioning based image compression using quality measures for subdivision decision

This paper presents new partitioning methods for image compression using different image quality measures, which are improvements of the recently published Binary Tree Triangular Coding (BTTC) algorithm. The technique is based on recursive partitioning of the image domain into right-angled triangles arranged in a binary tree. All the partitioning methods proposed in this paper execute in O( n log n ) time for encoding and θ ( n ) time for decoding, where n is the number of pixels in the image. Simulation results on standard test images show that the new methods produce significant improvement in quality as compared with conventional BTTC for comparable compression ratios.

TREE TRIANGULAR CODING IMAGE COMPRESSION ALGORITHMS

This paper presents new algorithms for image compression that are an improvement on the recently published Binary Tree Triangular Coding (BTTC). These algorithms are based on recursive decomposition of the image domain into triangles where the new triangle vertex is located at the point of maximum prediction error and does not require the constraints of right-angled isosceles triangle and square image as in previous algorithm. These algorithms execute in O(n log n) for encoding and θ(n) for decoding, where n is the number of image pixels. Simulation results show that the new algorithms have a significant execution time advantage over conventional BTTC while providing a quality of the reconstructed image as good as BTTC. This improvement is obtained by eliminating a major weakness of the standard BTTC, wherein the algorithm does not utilize the point of maximum error for domain decomposition despite performing an exhaustive search (in the worst case) over the triangular domain.

Improved image compression using S-tree and shading approach

Distasi et al. (see ibid., vol.45, p.1095-1100, 1997), presented a storage-saving image compression method called the B-tree triangular coding (BTTC) method. Based on the modified S-tree data structure and the Gouraud shading method, this paper presents an improved image compression method railed the S-tree compression (STC) method. Experimental results illustrate that the bit rates and the image quality of the proposed STC method are quite competitive with the BTTC method, Due to the simple geometrical decomposition in the STC method, the ratio of the execution time or the proposed method over the BTTC method is less than 1/2.

Image compression by B-tree triangular coding

This paper describes an algorithm for still image compression called B-tree triangular coding (BTTC). The coding scheme is based on the recursive decomposition of the image domain into right-angled triangles arranged in a binary tree. The method is attractive because of its fast encoding, O(n log n), and decoding, /spl Theta/(n), where n is the number of pixels, and because it is easy to implement and to parallelize. Experimental studies indicate that BTTC produces images of satisfactory quality from a subjective and objective point of view, One advantage of BTTC over JPEG is its shorter execution time.

Forcing Linearity on Greedy Codes

Described in this paper are two different methods of forcing greedy codes to be linear over arbitrary finite fields. Both methods are generalizations of the binary B-greedy codes as well as the triangular greedy codes over arbitrary fields. One method generalizes to arbitrary orderings over arbitrary finite fields while the other method generalizes theB -greedy codes to linear codes over arbitrary finite fields. Examples of the first method are computed for triangular greedy codes. These examples give codes similar to triangular codes from B-orderings. Both methods are shown to be substantially different.