1. CSCI 3280 Tutorial 6

2. Outline  Theory part of LZW  Tree representation of LZW  Table representation of LZW

3. Introduction  What is LZW?  Lossless compression method  Lempel-Ziv-Welch  Based on LZ78

4. Basic idea  Assume repetition of phase usually occurs  Use a code to represent one phase  Build a dictionary of phases that we met  If a phase is found in dictionary, use the code  If not found, add it to dictionary and give it a code  Very high compression ratio if lots of repetition

5. Algorithm  But how to handle byte stream?  The algorithm is similar to lecture note!  However, each node have maximum number of 256 child nodes. R 01 10 01 255 ….. R AssignmentLecture

6. R a b a b c d 0 255 ba ENCODER SIDE: R 979899100 c d …. Tree Structure Example

7. R a b a b c d 0 255 ba ENCODER SIDE: R 979899100 c d output: 97, b 256 …. Tree Structure Example

8. R a b a b c d 0 255 ba ENCODER SIDE: R 979899100 c d output: 97,98 b 256 …. 257 a Tree Structure Example

9. R a b a b c d 0 255 ba ENCODER SIDE: R 979899100 c d output: 97,98,256 b 256 …. 257 a 258 c Tree Structure Example

10. R a b a b c d 0 255 ba ENCODER SIDE: R 979899100 c d output: 97,98,256,99 b 256 …. 257 a 258 c 259 d Tree Structure Example

11. R a b a b c d 0 255 ba ENCODER SIDE: R 979899100 c d output: 97,98,256,99,100Encode complete! b 256 …. 257 a 258 c 259 d Tree Structure Example

12. R 0 255 ba DECODE SIDE: R 979899100 c d …. output: input: 97,98,256,99,100 Tree Structure Example

13. R 0 255 ba DECODE SIDE: R 979899100 c d …. output: a input: 97,98,256,99,100 Tree Structure Example

14. R 0 255 ba DECODE SIDE: R 979899100 c d …. output: a b input: 97,98,256,99,100 Last string Last string = a b 256 Tree Structure Example

15. R 0 255 ba DECODE SIDE: R 979899100 c d …. output: a b a b input: 97,98,256,99,100 Last string Last string = b b 256 257 a Tree Structure Example

16. R 0 255 ba DECODE SIDE: R 979899100 c d …. output: a b a b c input: 97,98,256,99,100 Last string Last string = a b b 256257 a 258 c Tree Structure Example

17. R 0 255 ba DECODE SIDE: R 979899100 c d …. output: a b a b c d input: 97,98,256,99,100 Last string Last string = c b 256257 a 258 c 259 d Tree Structure Example

18. Algorithm  Now let’s see a table structure example

19. IN: a b c c c d c c d CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 :: OUT: Prefix Char. Search Code Saved NULL Table Structure Compression

20. IN: a b c c c d c c d CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 :: OUT: Prefix Char. Search Code Saved NULL Table Structure Compression ‘a’ “a” 97 “a” ‘b’ “ab” 256 “ ab ” 97

21. IN: a b c c c d c c d CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 256 “ ab ” OUT: 97, Prefix Char. Search Code Saved NULL ‘b’ “b” 98 ‘b’ ‘c’ “bc” 257 “ bc ” 98 Table Structure Compression

22. IN: a b c c c d c c d CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 256 “ ab ” 257 “ bc ” OUT: 97, 98, Prefix Char. Search Code Saved NULL ‘c’ “c” 99 ‘c’ “cc” 258 “ cc ” 99 Table Structure Compression

23. IN: a b c c c d c c d CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 256 “ ab ” 257 “ bc ” 258 “ cc ” OUT: 97, 98, 99, Prefix Char. Search Code Saved NULL ‘c’ “c” 99 ‘c’ “cc” 258 ‘cc’ ‘d’ “ccd” 259 “ ccd ” 258 Table Structure Compression

24. IN: a b c c c d c c d CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 256 “ ab ” 257 “ bc ” 258 “ cc ” 259 “ ccd ” OUT: 97, 98, 99, 258, Prefix Char. Search Code Saved NULL ‘d’ “d” 100 ‘d’ ‘c’ “dc” 260 “ dc ” 100 Table Structure Compression

25. IN: a b c c c d c c d CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 256 “ ab ” 257 “ bc ” 258 “ cc ” 259 “ ccd ” 260 “ dc ” OUT: 97, 98, 99, 258, 100, Prefix Char. Search Code Saved NULL ‘c’ “c” 99 ‘c’ “cc” 258 ‘cc’ ‘d’ “ccd” 259 Table Structure Compression

26. IN: 97, 98, 99, 258, 100, 259 CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 OUT: cW pW C C dict(pW)+C 97 a Table Structure Decompression

27. IN: 97, 98, 99, 258, 100, 259 CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 OUT: a “ab” 256 b cW pW C C dict(pW)+C 98 97‘b’ “ab” Table Structure Decompression

28. IN: 97, 98, 99, 258, 100, 259 CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 256 “ ab ” OUT: a b “bc” 257 c cW pW C C dict(pW)+C 99 98‘c’ “bc” Table Structure Decompression

29. IN: 97, 98, 99, 258, 100, 259 CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 256 “ ab ” 257 “ bc ” OUT: a b c “cc” 258 c cW pW C C dict(pW)+C 258 99‘c’ “cc” exception Table Structure Decompression

30. IN: 97, 98, 99, 258, 100, 259 CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 256 “ ab ” 257 “ bc ” 258 “ cc ” OUT: a b c c c “ccd” 259 d cW pW C C dict(pW)+C 100 258‘d’ “ccd” Table Structure Decompression

31. IN: 97, 98, 99, 258, 100, 259 CODEEntry 0NUL : 97a 98b 99c 100d :: 255ASCII-255 256 “ ab ” 257 “ bc ” 258 “ cc ” 259 “ ccd ” OUT: a b c c c d “dc” 260 c c d cW pW C C dict(pW)+C 259 100‘c’ “dc” Table Structure Decompression

32.  Handling of exception case:  Usually C is the first char of current word(cW)  In exception C is the first char of previous word(pW)

33. Exercise  Encode and decode with tree structure. (This helps to better understand that in exception case, why C must be the first char of pW.)  My understanding to the exercise question: To encounter exception case, cW must be construct along pW branch, otherwise we will not encounter exception case, so the first char of cW and pW is the same char.