코딩 이론

수학노트
Pythagoras0 (토론 | 기여)님의 2021년 3월 17일 (수) 22:37 판 (→‎메타데이터: 새 문단)
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개요

  • 오류가 발생할 수 있는 정보의 송수신을 어떻게 하면 효율적으로 정확하게 할 것인가의 문제에서 기원.
    • 클로드 섀넌의 정보이론
  • 수학적으로는 유한체 위의 선형대수학
  • 유한단순군, 이차형식과 밀접하게 연관되어 있음.



선수 과목 또는 알고 있으면 좋은 것들



중요한 개념 및 정리

  • 코드
    • 이차형식에서 격자에 대응
  • 코드의 weight enumerator
    • 격자의 쎄타함수에 대응
  • 코드 : 격자 = 코드의 weight enumerator : 격자의 세타함수
  • 오류정정코드
  • 코드의 weight enumerator
  • 맥윌리엄스 항등식 (MacWilliams Identity)



코드의 예

다른 과목과의 관련성



메모



역사


관련된 항목들


관련된 대학원 과목 또는 더 공부하면 좋은 것들


표준적인 교과서



관련도서


리뷰, 에세이, 강의노트

관련논문

노트

말뭉치

  1. In most cases, such as in the Goldreich-Levin hard-core predicate construction, the coding theory interpretation became clear only in retrospect, but then it was essential for further improvements.[1]
  2. Coding theory is the branch of mathematics concerned with transmitting data across noisy channels and recovering the message.[2]
  3. Coding theory is about making messages easy to read: don't confuse it with cryptography which is the art of making messages hard to read![2]
  4. Not only has coding theory helped to solve problems of vital importance in the world outside mathematics, it has enriched other branches of mathematics, with new problems as well as new solutions.[2]
  5. Coding theory is the study of the properties of codes and their respective fitness for specific applications.[3]
  6. The purpose of channel coding theory is to find codes which transmit quickly, contain many valid code words and can correct or at least detect many errors.[3]
  7. A code which is a subspace of that linear space is called a linear code, which codes are of special importance in coding theory and turn out to be interesting from a geometric point of view.[4]
  8. Coding theory, sometimes called algebraic coding theory, deals with the design of error-correcting codes for the reliable transmission of information across noisy channels.[5]
  9. Here is a book in writing that develops the fundamental aspects of coding theory in a gentle manner.[6]
  10. Starting from the basics of coding theory and some of the classic theorems of the subject, the course will discuss more recent progress on code constructions and error-correction algorithms.[7]
  11. There are many good introductory books on coding theory (see partial list below), but none of them have the same focus and goals as the course.[7]
  12. We will cover several foundational methods that are widely used in modern research in coding theory and adjacent areas of CS and discrete mathematics.[8]
  13. The first part covers basic concepts of coding theory including linear codes and bounds on codes.[8]
  14. The course will take students to the forefront of research in some of the mentioned topics, enabling them to follow current research literature in coding theory and applications.[8]
  15. Sage provides an extensive library of objects and algorithms in coding theory.[9]
  16. Basic objects in coding theory are codes, channels, encoders, and decoders.[9]
  17. Over the past few decades, the term coding theory has become associated predominantly with error correcting codes.[10]
  18. A good part of this course will be devoted to coding theory.[10]
  19. The beginning: Claude Shannons 1948 paper A Mathematical Theory of Communication marks the birth of a new subject called Information Theory, part of which is coding theory.[10]
  20. Thus, by the mid 1970s a very different form of common coding theory had become prevalent.[11]
  21. This book is intended to attract the attention of practitioners and researchers in academia and industry interested in challenging paradigms of coding theory and computer vision.[12]
  22. The chapters in this comprehensive reference explore the latest developments, methods, approaches, and applications of coding theory in a wide variety of fields and endeavours.[12]
  23. All the chapters are authored by various researchers around the world covering the field of coding theory and image and video processing.[12]
  24. This book mainly focusses on researchers who can do quality research in the area of coding theory and image and video processing and related fields.[12]
  25. After introducing coding theory and linear codes these notes concern topics mostly from algebraic coding theory.[13]
  26. One of the most important key technologies for digital communication systems as well as storage media is coding theory.[14]
  27. Algorithms, Architectures and Applications provides a concise overview of channel coding theory and practice, as well as the accompanying signal processing architectures.[14]
  28. The book is unique in presenting algorithms, architectures, and applications of coding theory in a unified framework.[14]
  29. It covers the basics of coding theory before moving on to discuss algebraic linear block and cyclic codes, turbo codes and low density parity check codes and space-time codes.[14]
  30. Fueled by these new scenarios, coding theory remains a rapidly advancing area of research.[15]
  31. One trend in many of these new scenarios in coding theory is the need for algorithmic solutions.[15]
  32. For many problems in coding theory, it is possible to come up with nearly optimal solutions (information-theoretically speaking) which are likely very hard for Alice and Bob to actually implement.[15]
  33. The goal of algorithmic coding theory is to design solutions which are not only combinatorially good, but are also computationally efficient.[15]
  34. Coding theory stands as a cornerstone for most of computer science.[16]
  35. This three-part series of blog posts describes what coding theory is and delves into Richard Hamming’s contributions.[16]
  36. If a person truly comprehends Hamming’s work, they can fully appreciate coding theory and its significance to computer science.[16]
  37. This first installment of the series defines coding theory, error detecting codes, and error correcting codes.[16]
  38. Offers a discussion of coding theory, which is often covered in today’s cryptology courses.[17]
  39. Through a rich, mathematically elegant set of techniques, coding theory has come to significantly influence the design of modern data communications, compression and storage systems.[18]
  40. Predictive coding theory is a mechanistic theory: it aims to describe the neurocomputational machinery.[19]
  41. We consider this question as a central issue of the predictive coding theory.[19]

소스

  1. ↑ C294 Coding Theory and Complexity Theory
  2. ↑ 2.0 2.1 2.2 Coding theory: the first 50 years
  3. ↑ 3.0 3.1 Coding theory
  4. ↑ Coding Theory - an overview
  5. ↑ Coding Theory -- from Wolfram MathWorld
  6. ↑ Introduction to Coding Theory, Winter 2010.
  7. ↑ 7.0 7.1 Introduction to Coding Theory, Winter 2010.
  8. ↑ 8.0 8.1 8.2 Coding Theory and Applications
  9. ↑ 9.0 9.1 Coding Theory — Sage 9.2 Reference Manual: Coding Theory
  10. ↑ 10.0 10.1 10.2 What is coding theory and what is cryptography?
  11. ↑ Mental Imagery > Dual Coding and Common Coding Theories of Memory (Stanford Encyclopedia of Philosophy)
  12. ↑ 12.0 12.1 12.2 12.3 Coding Theory
  13. ↑ J. H. van Lint
  14. ↑ 14.0 14.1 14.2 14.3 Coding Theory: Algorithms, Architectures and Applications
  15. ↑ 15.0 15.1 15.2 15.3 Algorithmic Coding Theory
  16. ↑ 16.0 16.1 16.2 16.3 Coding Theory (Part 1 Of 3) - Coding Theory Defined
  17. ↑ Trappe & Washington, Introduction to Cryptography with Coding Theory
  18. ↑ ICML 2019
  19. ↑ 19.0 19.1 Is predictive coding theory articulated enough to be testable?

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