Problem sheet lecture video 2 PDF

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Technische Universität München Institute for Media Technology Prof. Dr.-Ing. Eckehard Steinbach

Image and Video Compression Summer Semester 2020

Problem sheet after Lecture Video 2 prepared by Furkan Kaynar

Tutorial I Problem 1: Variable Length Codes Determine if the following codes are uniquely decodable. Which ones are prefix codes? 𝜶𝒊 𝜶𝟏 𝜶𝟐 𝜶𝟑 𝜶𝟒 𝜶𝟓 𝜶𝟔 𝜶𝟕 𝜶𝟖

Code word 0 10 11 101 111 0010 0111 1001

𝜶𝒊 𝜶𝟏 𝜶𝟐 𝜶𝟑 𝜶𝟒 𝜶𝟓 𝜶𝟔 𝜶𝟕 𝜶𝟖

Code word 01 000 110 100 111 1010 1011 0011

𝜶𝒊 𝜶𝟏 𝜶𝟐 𝜶𝟑 𝜶𝟒 𝜶𝟓 𝜶𝟔 𝜶𝟕 𝜶𝟖

Code word 0 01 011 0111 01111 011111 0111111 01111111

Problem 2: Information Theory Basics For an arbitrary random variable 𝑋 with an alphabet 𝐴𝑋 a. Show that 0 ≤ 𝐻(𝑋). Under which conditions does equality hold? b. Is it possible for the equality 𝐻(𝑋) = 𝑙𝑜𝑔2 (‖𝐴𝑋 ‖) to be fulfilled? Problem 4: Conditional Entropy Given the sequence abracadabra$. a. Determine the conditional Huffman code table (assume a Markov-1 source). Hint: Determine the necessary PMFs by analyzing the entire string. b. Calculate the average code word length. c. How large is the redundancy of the code? d. Encode the sequence using the table of (a) and verify (b). e. Decode the bitstream a 01010111, where a denotes the bits representing ‘a’....