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COMP2610/6261 - Information Theory Lecture 17: Lempel-Ziv Coding and Summary ANU Logo Use Guidelines Mark Reid and Aditya Menon ResearchSchoolofComputerScience The ANU logo is a contemporary TheAustralianNationalUniversity reflection of our heritage. It clearly presents our name, our shield and our motto: First to learn the nature of things. To preserve the authenticity of our brand identity, there are rules that govern how our logo is used. SePrpefertrede lomgo ber 30th, 2014 Black version Preferred logo - horizontal logo The preferred logo should be used on a white background. This version includes black text with the crest in Deep Gold in either PMS or CMYK. Black Where colour printing is not available, the black logo can be used on a white background. Reverse MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 1/12 The logo can be used white reversed out of a black background, or occasionally a neutral dark background. Deep Gold Black C30 M50 Y70 K40 C0 M0 Y0 K100 PMS Metallic 8620 PMS Process Black PMS 463 Reverse version Any application of the ANU logo on a coloured background is subject to approval by the Marketing Office, contact [email protected] 1 LOGO USE GUIDELINES THE AUSTRALIAN NATIONAL UNIVERSITY 1 Lempel-Ziv Coding 2 Compression Review MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 2/12 Run-length coding using (count,symbol) saves 12 bits: 111 0 111 1 111 0 111 1 (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) 7 a 7 b 7 a 7 b Makes no probabilistic assumptions about source. Doesn’t always yield shorter strings: aa bb a b a → 10 0 10 1 01 0 01 1 01 0 (7 to 15 bits) Misses other structure: “2 repetitions of (7 as and 7 bs)” Eliminating Repetition What is a simple, short binary description of the following string? aaaaaaa bbbbbbb aaaaaaa bbbbbbb (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) 7as 7bs 7as 7bs A simple symbol code for {a,b}, C = {0,1}, uses 28 bits MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 3/12 Makes no probabilistic assumptions about source. Doesn’t always yield shorter strings: aa bb a b a → 10 0 10 1 01 0 01 1 01 0 (7 to 15 bits) Misses other structure: “2 repetitions of (7 as and 7 bs)” Eliminating Repetition What is a simple, short binary description of the following string? aaaaaaa bbbbbbb aaaaaaa bbbbbbb (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) 7as 7bs 7as 7bs A simple symbol code for {a,b}, C = {0,1}, uses 28 bits Run-length coding using (count,symbol) saves 12 bits: 111 0 111 1 111 0 111 1 (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) 7 a 7 b 7 a 7 b MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 3/12 Eliminating Repetition What is a simple, short binary description of the following string? aaaaaaa bbbbbbb aaaaaaa bbbbbbb (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) 7as 7bs 7as 7bs A simple symbol code for {a,b}, C = {0,1}, uses 28 bits Run-length coding using (count,symbol) saves 12 bits: 111 0 111 1 111 0 111 1 (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) 7 a 7 b 7 a 7 b Makes no probabilistic assumptions about source. Doesn’t always yield shorter strings: aa bb a b a → 10 0 10 1 01 0 01 1 01 0 (7 to 15 bits) Misses other structure: “2 repetitions of (7 as and 7 bs)” MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 3/12 1 A new a 2 A new b 3 The same 1 symbol as 1 symbol ago 4 The same 2 symbols as 3 symbols ago 5 The same 10 symbols as 5 symbols ago 00 01 10010001 10110010 11011001 ... Looking for Repetition Consider a sequence that starts abbababbababbab... We can describe each new part in terms of what we have seen so far: MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 4/12 2 A new b 3 The same 1 symbol as 1 symbol ago 4 The same 2 symbols as 3 symbols ago 5 The same 10 symbols as 5 symbols ago 00 01 10010001 10110010 11011001 ... Looking for Repetition Consider a sequence that starts abbababbababbab... We can describe each new part in terms of what we have seen so far: 1 A new a MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 4/12 3 The same 1 symbol as 1 symbol ago 4 The same 2 symbols as 3 symbols ago 5 The same 10 symbols as 5 symbols ago 00 01 10010001 10110010 11011001 ... Looking for Repetition Consider a sequence that starts abbababbababbab... We can describe each new part in terms of what we have seen so far: 1 A new a 2 A new b MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 4/12 4 The same 2 symbols as 3 symbols ago 5 The same 10 symbols as 5 symbols ago 00 01 10010001 10110010 11011001 ... Looking for Repetition Consider a sequence that starts abbababbababbab... We can describe each new part in terms of what we have seen so far: 1 A new a 2 A new b 3 The same 1 symbol as 1 symbol ago MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 4/12 5 The same 10 symbols as 5 symbols ago 00 01 10010001 10110010 11011001 ... Looking for Repetition Consider a sequence that starts abbababbababbab... We can describe each new part in terms of what we have seen so far: 1 A new a 2 A new b 3 The same 1 symbol as 1 symbol ago 4 The same 2 symbols as 3 symbols ago MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 4/12

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COMP2610/6261 - Information Theory Lecture 17: Lempel-Ziv Coding and Summary ANU Logo Use Guidelines Mark Reid and Aditya Menon ResearchSchoolofComputerScience The ANU logo is a contemporary TheAustralianNationalUniversity reflection of our heritage. It clearly presents our name, our shield and our motto: First to learn the nature of things. To preserve the authenticity of our brand identity, there are rules that govern how our logo is used. SePrpefertrede lomgo ber 30th, 2014 Black version Preferred logo - horizontal logo The preferred logo should be used on a white background. This version includes black text with the crest in Deep Gold in either PMS or CMYK. Black Where colour printing is not available, the black logo can be used on a white background. Reverse MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 1/12 The logo can be used white reversed out of a black background, or occasionally a neutral dark background. Deep Gold Black C30 M50 Y70 K40 C0 M0 Y0 K100 PMS Metallic 8620 PMS Process Black PMS 463 Reverse version Any application of the ANU logo on a coloured background is subject to approval by the Marketing Office, contact [email protected] 1 LOGO USE GUIDELINES THE AUSTRALIAN NATIONAL UNIVERSITY 1 Lempel-Ziv Coding 2 Compression Review MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 2/12 Run-length coding using (count,symbol) saves 12 bits: 111 0 111 1 111 0 111 1 (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) 7 a 7 b 7 a 7 b Makes no probabilistic assumptions about source. Doesn’t always yield shorter strings: aa bb a b a → 10 0 10 1 01 0 01 1 01 0 (7 to 15 bits) Misses other structure: “2 repetitions of (7 as and 7 bs)” Eliminating Repetition What is a simple, short binary description of the following string? aaaaaaa bbbbbbb aaaaaaa bbbbbbb (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) 7as 7bs 7as 7bs A simple symbol code for {a,b}, C = {0,1}, uses 28 bits MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 3/12 Makes no probabilistic assumptions about source. Doesn’t always yield shorter strings: aa bb a b a → 10 0 10 1 01 0 01 1 01 0 (7 to 15 bits) Misses other structure: “2 repetitions of (7 as and 7 bs)” Eliminating Repetition What is a simple, short binary description of the following string? aaaaaaa bbbbbbb aaaaaaa bbbbbbb (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) 7as 7bs 7as 7bs A simple symbol code for {a,b}, C = {0,1}, uses 28 bits Run-length coding using (count,symbol) saves 12 bits: 111 0 111 1 111 0 111 1 (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) 7 a 7 b 7 a 7 b MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 3/12 Eliminating Repetition What is a simple, short binary description of the following string? aaaaaaa bbbbbbb aaaaaaa bbbbbbb (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) 7as 7bs 7as 7bs A simple symbol code for {a,b}, C = {0,1}, uses 28 bits Run-length coding using (count,symbol) saves 12 bits: 111 0 111 1 111 0 111 1 (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) (cid:124)(cid:123)(cid:122)(cid:125)(cid:124)(cid:123)(cid:122)(cid:125) 7 a 7 b 7 a 7 b Makes no probabilistic assumptions about source. Doesn’t always yield shorter strings: aa bb a b a → 10 0 10 1 01 0 01 1 01 0 (7 to 15 bits) Misses other structure: “2 repetitions of (7 as and 7 bs)” MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 3/12 1 A new a 2 A new b 3 The same 1 symbol as 1 symbol ago 4 The same 2 symbols as 3 symbols ago 5 The same 10 symbols as 5 symbols ago 00 01 10010001 10110010 11011001 ... Looking for Repetition Consider a sequence that starts abbababbababbab... We can describe each new part in terms of what we have seen so far: MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 4/12 2 A new b 3 The same 1 symbol as 1 symbol ago 4 The same 2 symbols as 3 symbols ago 5 The same 10 symbols as 5 symbols ago 00 01 10010001 10110010 11011001 ... Looking for Repetition Consider a sequence that starts abbababbababbab... We can describe each new part in terms of what we have seen so far: 1 A new a MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 4/12 3 The same 1 symbol as 1 symbol ago 4 The same 2 symbols as 3 symbols ago 5 The same 10 symbols as 5 symbols ago 00 01 10010001 10110010 11011001 ... Looking for Repetition Consider a sequence that starts abbababbababbab... We can describe each new part in terms of what we have seen so far: 1 A new a 2 A new b MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 4/12 4 The same 2 symbols as 3 symbols ago 5 The same 10 symbols as 5 symbols ago 00 01 10010001 10110010 11011001 ... Looking for Repetition Consider a sequence that starts abbababbababbab... We can describe each new part in terms of what we have seen so far: 1 A new a 2 A new b 3 The same 1 symbol as 1 symbol ago MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 4/12 5 The same 10 symbols as 5 symbols ago 00 01 10010001 10110010 11011001 ... Looking for Repetition Consider a sequence that starts abbababbababbab... We can describe each new part in terms of what we have seen so far: 1 A new a 2 A new b 3 The same 1 symbol as 1 symbol ago 4 The same 2 symbols as 3 symbols ago MarkReidandAdityaMenon (ANU) COMP2610/6261-InformationTheory September30th,2014 4/12

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