114_1_image_proc_exam_2008_Part2

114_1_image_proc_exam_2008_Part2 - In other words, if a...

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EE114D Introduction to Speech and Image Processing Winter Quarter, 2008 Page 3 of 3 5. Huffman Coding (20 points) Consider the performance of a basketball team that is participating in a tournament with 16 teams. The tournament is single elimination – in other words, in the first round of play, all 16 teams participate. The 8 winning teams advance to the 2 nd round (which in this example is also called the quarter finals). The 4 teams that win in the quarter finals advance to the semi finals. The two teams that win in the semi finals play each other in the finals, and the winner of that final game is the winner of the tournament. Assume that the probability of a team winning or losing each game is exactly 1/2 (there is no draw), and that the game results are independent of one another.
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Unformatted text preview: In other words, if a team wins one game and advances to the next round, its probability of winning the next game is 1/2. There are five possible outcomes for a basketball team in such a tournament. These outcomes can be indicated using the letters A through E with the following meanings: A: Team loses in the 1 st round B: Team advances up to the quarter finals, but loses in the quarter finals C: Team advances up to the semi finals, but loses in the semi finals D: Team advances up to the finals, but loses in the finals E: Team wins the tournament Thus, the symbol alphabet is A through E. a) (10 points) Calculate the entropy of this source. b) (10 points) Design a Huffman code for this source. Find the efficiency of the Huffman code....
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