499/599 ECE Data Compression/Information Theory Spring 06 Dr. Thinh Nguyen Homework 2 Due 04/27/06 at the beginning of the class
Problem 1: Do problem 4 in chapter 3 of the textbook. (6pts) Problem 2: Suppose you are given a task of compressing a Klingon text consisting of 10,000 letters. To your surprise, the Klingon alphabet consists of only five different letters: k1, k2, k3, k4, and k5. Furthermore, you notice that there are 4000 k1s, 3000 k2s, 2000 k3s, 500 k4s and 500 k5s. (6pts) (a) Develop the Huffman codes for these Klingon letters. (b) What is the average code rate? (c) Interestingly, you notice that the letters k4 and k5 always appear together as k4k5. Can you use this information to improve the compression ratio? If so, what are the new codes and corresponding average coding rate? Problem 3: By now, you are an expert at compressing aliens languages, the U.S. government assigns you the task of compressing Krypton language. Kryptonite are very smart (or stupid) beings, as such their entire language can be represented by sequences consisting of only three letters k1, k2, and k3. Being a compression expert that you are, you exam the krypton text, and notice there are 7000 2000 k1s, k2s, and 1000 k3s out of the given Krypton text containing 10,000 letters. (6pts) (a) What is the entropy rate of this Krypton text? (b) If Huffman code is used to code the letters, what is the average code rate? (c) Due to the bandwidth limitation of inter-star communication, the US government wants you to improve your basic Huffman compression scheme. Can you modify Huffman coding to compress the Krypton text further? If so, provide an example of the new codes. Problem 4: (bonus) Suppose you are at Las Vegas, and you notice this one peculiar game. The game is described as follows. A guy throws a perculiar dice with three faces: 1, 2, and 3. However, he would not let you know the outcome of the di...