John R Woodward How can we transmit a signal from one point to another ensuring minimal error What is more if we detect an error how can we potentially recover the original signal In this talk we will look at a branch of mathematics and computer science called coding theory We wil ID: 1034781
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1. Kodz: a brief look at coding theory.John R. Woodward How can we transmit a signal from one point to another ensuring minimal error? What is more, if we detect an error, how can we potentially recover the original signal? In this talk, we will look at a branch of mathematics and computer science called coding theory. We will look at some of the basic concepts such as error checking and error correcting code. These ideas will be illustrated with some examples from everyday situations.Note use presenter view. 1
2. What do the following have in common2
3. Analogy vs Digital3
4. continuousDiscrete 4
5. Lets transmita signal1/ analogy2/ digital5
6. We do not verbalize punctuation dot the i's and cross the t'sdot the is and cross the tsString of 0s and 1sString of 0’s and 1’sWe do not differentiate between these when we speak. 6
7. Grrr?Boys school Mens haircutsVisitors carparkMagistrates courtWhere does the apostrophe go??7
8. Vowels and Consonants Vowels – messageConsonants – emotion/accent. It is not what you say it is the way you say it WikiAudio https://www.youtube.com/watch?v=-dYJ0u4U9aQ8
9. What do the following sentences say. Th qck brwn fx jmps vr th lzy dg lv prs n th sprngtm. Y cn d nythng bt nt vrythng.9
10. answersThe quick brown fox jumped over the lazy dogs. I love Paris in the springtime. You can do anything but not everything. 10
11. Morse code tree11
12. Morse code tree… --- … 2) --- -- --. 12
13. Morse code tree – no reducdancy… --- … SOS 2) --- -- --. OMG13
14. English is not PerfectEssay – SA. homophonesRead – past and present. Phonetics code. Each sound has one symbolsRecord record (noun and verb – import export) mark stress. English alphabet is a poor encoding of soundsHow would you say ghoti. 14
15. Ghoti = fishgh = /f/ as in enough. o = /i/ as in women. ti= /sh/ as in nation.15
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19. Hypothesis - phonetic languages Do phonetic languages have less jokes. Do phonetic languages have more consistent pronunciation?Is dyslexia as common in countries with phonetic languages. 19
20. Redundancy in Natural LanguageHe put his hands in his pockets彼は彼のポケットに彼の手を入れた彼はポケットに彼の手を入れた彼はポケットに手を入れたポケットに手を入れた20
21. Emergency Numbers999 UK911 in USA119 in JapanMobile phone numbers are separated. 21
22. EXPT: misdial a mobile number – you probably do not get a valid number22
23. True/false 0/1Students need to transmit the following info. Exam – question on binary arithmeticAnswers were 0 or 1Exam – questions on logic Answers are T or F (of course True/False)23
24. Drawing a cube01A line 1st digit0=left, 1=right00100111A square.2nd digit0=bottom1=top000100010110001101011111A cube.3rd digit0=front,1=backFor example 010 = Left, top, front.Think of coordinates in 3 dimensionsThe process is as follow;Draw a line – label each end 0, 1. Make a copy of this and join corresponding vertexes. Add a new coordinate 0 or 1. Repeat this process.24
25. 00001000010011000010101001101110000110010101110100111011011111114th bit = inside or outside cube25
26. 1 bit – cannot tell if we made a mistake01A line 1st digit0=left, 1=right26
27. 2 bits – we can detect mistakes, but cannot correct00100111A square.2nd digit0=bottom1=top27
28. 3 bits – we can correct000100010110001101011111A cube.3rd digit0=front,1=backWordsYESNO28
29. 3 bits – DISTANCE ONE APART000100010110001101011111A cube.3rd digit0=front,1=backCODE WORDSWordsYESNO29
30. 3 bits – DISTANCE TWO APART000100010110001101011111A cube.3rd digit0=front,1=backCODE WORDSWordsYESNO30
31. 3 bits – DISTANCE THREE APART000100010110001101011111A cube.3rd digit0=front,1=backCODE WORDSWordsYESNO31
32. 1 = yes 0 = noCODE AS 111= YES, 000 = NO32
33. What if there is a mistake33
34. Perfect code34
35. In 7 dimension35
36. 7 edges going out36
37. Genetic Code 14 BASES A-U C-G20 AMINO ACIDS37
38. Genetic CodeGenetic Code 238
39. Genetic Code 3No gapsUse 3 bases (ATCG) not 2 or 4 for 21 code words (20 amino acids + stop)Instantaneous – needed! Even if mistake is made in last base – often okay – grouped (locality/redundancy)Even if wrong amino acid – still has similar chemical properties. 39
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41. Working in a bar41Teacher : touch the left wall
42. McGurk EffectSay “bar”Lips “far or bar”https://youtu.be/G-lN8vWm3m0?t=1m15s 42
43. Add a Parity Bit to a messagePar = equalParity is zero (false) for EVEN 0, 2, 4, 6, ….Parity is one (true) for ODD 1, 3, 5, …MESSAGE = 1011The “total” = 3, which is odd, parity is 1Supplemented message = 10111An extra “1” is added43
44. Following messageIs the following message corrupted?0101144
45. Following messageIs the following message corrupted?01011The message is 0101, (first 4 bits)sums to 2 (= 0+1+0+1)which is EVENSo parity should be 0We see 01011 but expected 10100 (???)45
46. To detect AND correctWe need to add more parity bits4 data bits3 parity bits46
47. Parity of 3 data bits in circle47
48. Standard sequence (D=data, P=parity)48
49. Parity is consistent. 49
50. OOPS we have a single error50
51. 2 or more parity bits will be incorrect51
52. intersection tells us the corrupted bit52
53. Parity bits carry no new information53
54. Shortcut for hamming codehttps://www.youtube.com/watch?v=JAMLuxdHH8o54
55. Perceptronsmalefemale55
56. Linearly Separable Data +Non-Linearly Separable Data +Assessment markExam mark56
57. XOR PROBLEM00100111Can you draw a straight line to separate the ticks and crosses57
58. Add a parity bit.00010101111058
59. Now plot in 3D000100010110001101011111A cube.3rd digit0=front,1=backCan weSeparateWith aLine now59
60. Join 4 cities with the least road lengthXXXX60
61. Join 4 cities with the least road lengthXXXX61
62. Join 4 cities with the least road lengthXXXX62
63. Join 4 cities with the least road lengthXXXX63
64. solution64
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66. 20 questionsYou can ask yes/no questions. Not L/RWhat is a good question? Phone bookHow many questions on average? Can use it as a code.This is not proved in machine learning books. 66
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69. Richard HammingRichard Wesley Hamming was an American mathematician whose work had many implications for computer engineering and telecommunications. WikipediaBorn: 11 February 1915, Chicago, Illinois, United StatesDied: 7 January 1998, Monterey, California, United StatesField: MathematicsEducation: University of Illinois at Chicago (1942), University of Nebraska–Lincoln (1939), University of Chicago (1937)Awards: Turing Award, IEEE Emanuel R. Piore Award69
70. Books 70