118 research outputs found
Nonlinear q-ary codes : constructions and minimum distance computation
Treball inclรฒs a la publicaciรณ que recull les contribucions al XIII Encuentro de รlgebra Computacional y AplicacionesA nonlinear code can be represented as the union of cosets of a linear subcode. Properties and constructions of new codes from given ones in terms of this representation can be described. Algorithms to compute the minimum distance of nonlinear codes, based on known algorithms for linear codes, are also established. Moreover, the performance of these algorithms is studied and an estimation of the number of enumerated codewords needed in the computations is given
์ต๋ ์ ์ด ํ ๋ฌ์ค ํจ์น๋ฅผ ์ด์ฉํ ํจ์จ์ ์ธ ๊ธฐํํ์ ์๊ณ ๋ฆฌ์ฆ
ํ์๋
ผ๋ฌธ(์์ฌ) -- ์์ธ๋ํ๊ต๋ํ์ : ๊ณต๊ณผ๋ํ ์ปดํจํฐ๊ณตํ๋ถ, 2021.8. ์์ํ.We present efficient geometric algorithms that are based upon toroidal patches. To begin with, we present to use osculating toroidal patches to approximate a regular surface and propose a reparametrization method for the approximating toroidal patches. Then, we show that the toroidal patches can approximate special kinds of freeform parametric surfaces that are built upon planar profil e curves much more effectively than general surfaces. Thanks to these precise toroidal patches, we can construct a very compact bounding volume hierarchy for a parametric surface. With the bounding volume hierarchy, we can perform fast and precise point projection, i.e., minimum distance computation from a point to the surface. Also, we can easily
find binormal lines, i.e. lines that connect two geometric entities orthogonally, between toroidal patches and use them to find meaningful distance measures for parametric surfaces. We show that we can fi nd such binormal lines easily by fi nding binormal lines between circles in space. Using these fundamental toroidal geometric operations, we present an efficient minimum distance computation algorithm for solids of revolution. This algorithm accelerates the minimum distance computation 10-100 times faster than conventional method. Also, we propose an efficient Hausdorff Distance computation algorithm that is applicable to various kinds of parametric surfaces. We can fi nd the Hausdorff Distance, almost up to machine precision, without much cost increase. Even though these algorithms follow conventional frameworks in large, they exhibit much better precision and efficiency than previous methods because of the toroidal patches that we use in our hierarchy.๋ณธ ๋
ผ๋ฌธ์์๋ ํ ๋ฌ์ค ํจ์น๋ฅผ ์ด์ฉํ ํจ์จ์ ์ธ ๊ธฐํํ์ ์๊ณ ๋ฆฌ์ฆ๋ค์ ์๊ฐํ๋ค. ๋จผ์ , ์์์ ์ผ๋ฐ์ ์ธ ์ ์น ๊ณก๋ฉด์ ๊ทผ์ฌํ๊ธฐ ์ํด ์ต๋ ์ ์ด ํ ๋ฌ์ค ํจ์น๋ฅผ ์ฌ์ฉํ ๊ฒ์ ์ ์ํ๋ค. ์ด๋ฅผ ์ํด ์ ์น ๊ณก๋ฉด์ ๋ณ์๋ฅผ ํ ๋ฌ์ค ํจ์น์ ๋ณ์๋ก ๋ณํํ๋ ์ฌ๋งค๊ฐํ ๊ณต์์ ์ ์ํ๋ค. ์ด์ ๋ํด, ํ ๋ฌ์ค ํจ์น๊ฐ ํ๋ฉด ๊ณก์ ์ ๊ธฐ๋ฐํ ํน์ํ ๊ณก๋ฉด๋ค์ ์ผ๋ฐ ๊ณก๋ฉด๋ค๋ณด๋ค ๋ ํจ๊ณผ์ ์ผ๋ก ๊ทผ์ฌํ ์ ์์์ ๋ณด์ธ๋ค.
์ด๋ฌํ ํ ๋ฌ์ค ํจ์น์ ์ ํ์ฑ ๋๋ถ์, ์์์ ๊ณก๋ฉด์ ๊ฐ์ธ๋ ๊ต์ฅํ ํจ์จ์ ์ธ bounding volume hierarchy๋ฅผ ์ป์ ์ ์๋ค. ์ด ์๋ฃ ๊ตฌ์กฐ๋ฅผ ์ด์ฉํ์ฌ ๊ณต๊ฐ ์์ ํ ์ ์์ ํด๋น ๊ณก๋ฉด์ผ๋ก์ ์ ํฌ์ ์ฐ์ฐ์ ๊ต์ฅํ ๋น ๋ฅด๊ณ ์ ํํ๊ฒ ํ ์ ์๋ค. ๋ํ, ๊ณก๋ฉด๋ค ์ฌ์ด์ ๋ค์ํ ๊ฑฐ๋ฆฌ๋ค์ ์ฐพ๊ธฐ ์ํด ์ด ์๋ฃ ๊ตฌ์กฐ์ ์ ์ฅ๋ ํ ๋ฌ์ค ํจ์น๋ค์ ์์ง์ผ๋ก ์ฐ๊ฒฐํ๋ binormal ์ง์ ์ ์ด์ฉํ ์ ์๋ค. ์ด๋ฌํ binormal ์ง์ ์ ํจ์จ์ ์ผ๋ก ์ฐพ๊ธฐ ์ํด ๊ณต๊ฐ ์์ ์๋ค์ ์ด์ฉํ ์ ์์์ ๋ณด์ธ๋ค.
ํ ๋ฌ์ค ํจ์น๊ฐ ์ ๊ณตํ๋ ์์ ๊ฐ์ ๊ธฐ์ด์ ์ธ ๊ธฐํํ์ ์ฐ์ฐ๋ค์ ํ ๋๋ก, ํจ์จ์ ์ธ ํ์ ์ฒด ์ฌ์ด์ ์ต๋จ ๊ฑฐ๋ฆฌ ๊ณ์ฐ ์๊ณ ๋ฆฌ์ฆ์ ์ ์ํ๋ค. ์ด ์๊ณ ๋ฆฌ์ฆ์ ๊ธฐ์กด์ ์๊ณ ๋ฆฌ์ฆ์ ๋นํด 10-100๋ฐฐ ๋น ๋ฅธ ์๋๋ก ์ต๋จ ๊ฑฐ๋ฆฌ๋ฅผ ๊ณ์ฐํ๋ค. ๋ํ, ํจ์จ์ ์ธ ํ์ฐ์ค๋๋ฅดํ ๊ฑฐ๋ฆฌ ๊ณ์ฐ ์๊ณ ๋ฆฌ์ฆ ์ญ์ ์ ์ํ๋ค. ์คํ ๊ฒฐ๊ณผ, ์ด ์๊ณ ๋ฆฌ์ฆ์ ํตํด ๊ฑฐ์ ๊ธฐ๊ณ ์ ํ๋ ๋ด์์ ์ ํํ ํ์ฐ์ค๋๋ฅดํ ๊ฑฐ๋ฆฌ๋ฅผ ํฐ ๋น์ฉ ์ฆ๊ฐ ์์ด ๊ณ์ฐํ ์ ์์๋ค. ์ด์ ๊ฐ์ ์ฑ๋ฅ ํฅ์์ ๋ณธ ๋
ผ๋ฌธ์์ ์ฌ์ฉํ ํ ๋ฌ์ค ํจ์น์ ์ ํ์ฑ๊ณผ ํจ์จ์ฑ์ ๊ธฐ๋ฐํ๊ณ ์๋ค.Chapter 1 Introduction 1
1.1 Background 1
1.2 Research Objectives and Contributions 4
1.3 Thesis Organization 6
Chapter 2 Preliminaries 7
2.1 Freeform Parametric Surface 7
2.1.1 B ezier Surface 8
2.1.2 Surface of Revolution 9
2.1.3 Surface of Linear Extrusion 10
2.2 Torus 11
Chapter 3 Related Work 13
3.1 Bounding Volume Hierarchy 13
3.2 Minimum Distance Computation 15
3.3 Hausdor Distance Computation 15
Chapter 4 Bounding Volume Hierarchy 17
4.1 Construction 17
4.2 Toroidal Patch Approximation 19
4.2.1 Regular surface 19
4.2.2 Surface of Revolution 23
4.2.3 Surface of Linear Extrusion 24
4.3 Toroidal Operations 25
4.3.1 Point Projection 25
4.3.2 Binormal Computation 27
Chapter 5 Geometric Algorithms 30
5.1 Minimum distance computation for solids of revolution 30
5.1.1 General Framework 30
5.1.2 Algorithm 31
5.1.3 Experimental Results 33
5.2 Hausdor Distance computation 37
5.2.1 General Framework 37
5.2.2 Algorithm 39
5.2.3 Experimental Results 42
Chapter 6 Conculsion 50
Appendices 52
Chapter A Torus reparametrization 53
Bibliography 60
์ด๋ก 67
Acknowledgments 68์
Efficient representation of binary nonlinear codes : constructions and minimum distance computation
Combinatorics, Coding and Security Group (CCSG)A binary nonlinear code can be represented as a union of cosets of a binary linear subcode. In this paper, the complexity of some algorithms to obtain this representation is analyzed. Moreover, some properties and constructions of new codes from given ones in terms of this representation are described. Algorithms to compute the minimum distance of binary nonlinear codes, based on known algorithms for linear codes, are also established, along with an algorithm to decode such codes. All results are written in such a way that they can be easily transformed into algorithms, and the performance of these algorithms is evaluated
Bringing Toric Codes to the next dimension
This paper is concerned with the minimum distance computation for higher
dimensional toric codes defined by lattice polytopes. We show that the minimum
distance is multiplicative with respect to taking the product of polytopes, and
behaves in a simple way when one builds a k-dilate of a pyramid over a
polytope. This allows us to construct a large class of examples of higher
dimensional toric codes where we can compute the minimum distance explicitly.Comment: 11 pages, 1 figure; Major changes in the section on parameters, new
examples
Efficient Maximum-Likelihood Decoding of Linear Block Codes on Binary Memoryless Channels
In this work, we consider efficient maximum-likelihood decoding of linear
block codes for small-to-moderate block lengths. The presented approach is a
branch-and-bound algorithm using the cutting-plane approach of Zhang and Siegel
(IEEE Trans. Inf. Theory, 2012) for obtaining lower bounds. We have compared
our proposed algorithm to the state-of-the-art commercial integer program
solver CPLEX, and for all considered codes our approach is faster for both low
and high signal-to-noise ratios. For instance, for the benchmark (155,64)
Tanner code our algorithm is more than 11 times as fast as CPLEX for an SNR of
1.0 dB on the additive white Gaussian noise channel. By a small modification,
our algorithm can be used to calculate the minimum distance, which we have
again verified to be much faster than using the CPLEX solver.Comment: Submitted to 2014 International Symposium on Information Theory. 5
Pages. Accepte
Safety-related Tasks within the Set-Based Task-Priority Inverse Kinematics Framework
In this paper we present a framework that allows the motion control of a
robotic arm automatically handling different kinds of safety-related tasks. The
developed controller is based on a Task-Priority Inverse Kinematics algorithm
that allows the manipulator's motion while respecting constraints defined
either in the joint or in the operational space in the form of equality-based
or set-based tasks. This gives the possibility to define, among the others,
tasks as joint-limits, obstacle avoidance or limiting the workspace in the
operational space. Additionally, an algorithm for the real-time computation of
the minimum distance between the manipulator and other objects in the
environment using depth measurements has been implemented, effectively allowing
obstacle avoidance tasks. Experiments with a Jaco manipulator, operating in
an environment where an RGB-D sensor is used for the obstacles detection, show
the effectiveness of the developed system
Block-Matching Optical Flow for Dynamic Vision Sensor- Algorithm and FPGA Implementation
Rapid and low power computation of optical flow (OF) is potentially useful in
robotics. The dynamic vision sensor (DVS) event camera produces quick and
sparse output, and has high dynamic range, but conventional OF algorithms are
frame-based and cannot be directly used with event-based cameras. Previous DVS
OF methods do not work well with dense textured input and are designed for
implementation in logic circuits. This paper proposes a new block-matching
based DVS OF algorithm which is inspired by motion estimation methods used for
MPEG video compression. The algorithm was implemented both in software and on
FPGA. For each event, it computes the motion direction as one of 9 directions.
The speed of the motion is set by the sample interval. Results show that the
Average Angular Error can be improved by 30\% compared with previous methods.
The OF can be calculated on FPGA with 50\,MHz clock in 0.2\,us per event (11
clock cycles), 20 times faster than a Java software implementation running on a
desktop PC. Sample data is shown that the method works on scenes dominated by
edges, sparse features, and dense texture.Comment: Published in ISCAS 201
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