S-72_2410_solution_3

S-72_2410_solution_3 - S-72.2410 Information Theory Haanp¨...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: S-72.2410 Information Theory Haanp¨ a¨a & Linja-aho Homework 3, solutions 2009 Homework 3, solutions Deadline: November 23rd, 16:00 The box for returning exercises is in the E-wing, 2nd floor corridor. 1. Apply the two Lempel-Ziv universal coding methods, LZ77 and LZ78, considered in the course to compress the following strings: 111000111000111000111111 110001110000111110000101 Also the compressed strings should be in binary format. Solution: LZ77 for the first string. The string is parsed: 1,110,001,110001110001111,11 and the codewords are (relative position of match, length of the match and first non-matching character): (0,0,1) (1,2,0) (1,2,1) (6,14,1) (1,1,1) For presenting the triplets in binary, we need three bits for the first value (max. value = 6), four bits for the second value (max. value = 14) and one bit for the last value: 000,0000,1 001,0010,0 001,0010,1 110,1110,1 001,0001,1 And for the second string: 1,10,001,110000,1111,1000010,1 (0,0,1) (1,1,0) (0,2,1) (6,5,0) (7,3,1) (9,5,0) (0,0,1) For presenting the triplets in binary, we need four bits for the first value (max. value = 9), three bits for the second value (max. value = 5) and one bit for the last value: 0000,000,1 0001,001,0 0000,010,1 0110,101,0 0111,011,1 1001,101,0 0000,000,1 Note: if you scan backwards and accept the first match (and do not look for the best possible match), you get a different solution and it is ok. There are many slightly different versions of the algorithm. LZ78 for the first string: 1,11,0,00,111,000,1110,001,1111,1 and the codewords (place of match in dictionary, and the non-matching character): (0,1) (1,1) (0,0) (3,0) (2,1) (4,0) (5,0) (4,1) (5,1) For the first value, we need three bits: 000,1 001,1 000,0 011,0 010,1...
View Full Document

This note was uploaded on 10/27/2010 for the course ECE 221 taught by Professor Sd during the Spring '10 term at Huston-Tillotson.

Page1 / 4

S-72_2410_solution_3 - S-72.2410 Information Theory Haanp¨...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online