Question 2 [total marks 15] a) i. For a source which uses a five symbol alphabet (A,B,C,D,E} there are five possible coding tree types which use combinations of codeword lengths between 1 and 3 bits, and which give uniquely decodable codes. Each of these tree types uses a different combination of 1-bit, 2-bit and 3-bit codeword lengths. Fixed length coding is the most straightforward but has the lowest coding efficiency because 3-bit codewords are assigned for each symbol. An example of this type of coding tree is shown below: five 3-bit codewords are used, there are 3 unused 3-bit codewords and no 1-bit or 2-bit codewords are used. Sketch an example of each of the other four types of coding tree. Your sketch should clearly show the combination of codeword lengths used but you do not need to assign binary codeword values. Only use 1-bit, 2-bit and 3-bit codewords. [4 marks] ii. A valid Huffman coding algorithm would only ever generate two of these possible coding tree types. State which two could be generated and explain why the others would not be generated by Huffman coding. [2 marks] iii. Explain what would determine which of the two valid Huffman coding trees would be generated in different cases i.e. why might one might be more efficient than the other for a specific case but it being the other way round in another case [2 mark] iv. Give a specific numerical example, with probabilities for each symbol, where each of these two Huffman codes would optimal. [2 mark]