Information Theory Homework 5: Lempel-Ziv Algorithm and Arithmetic Coding, Assignments of Electrical and Electronics Engineering

Download Information Theory Homework 5: Lempel-Ziv Algorithm and Arithmetic Coding and more Assignments Electrical and Electronics Engineering in PDF only on Docsity! ECE 6605 Information Theory HW #5: Assigned October 17 2003, due October 27,2003. 1) Lempel Ziv problem This problem concerns the Lempel-Ziv (LZ) data compression algorithm. Answer parts a) and b) below. The sources and codes in parts a) and b) are unrelated. a) Encoding. Given that the LZ encoder starts with the following table, construct the table and indicate the transmitted codewords for the source output X. You may assume that the source outputs either α or β. (You can number the codewords 1,2,3... ) X C(X) α β 1 2 Source output: X= α α α α β β α β β β α α α β α α α α b) Decoder. In this part you will be the decoder. Given the following sequence of codewords, decode it, and construct the table as you go along. You will start with the same table the encoder starts with and assume the source outputs two letters c and d. X C(X) 1 2 c d Codeword sequence to be decoded: 1 2 1 3 4 5 1 7 3 (decode this message and indicate whether this is a valid encoding. If it is not, give the correct codeword for the source output). 2) Arithmetic coding problem Consider a binary source that outputs a’s and b’s independently with probabilities P(a) = 0.1 and P(b) = 0.9 Using arithmetic coding, find the codeword for the following source output and compare it with the source entropy: a b a b b b a a