Discrete sources Assume a discrete memoryless source emits the possible symbols so, S1, S2, S3, S4 with the probabilities reported in the table below. (a) Define (mathematically and in words) the entropy of a discrete source, discuss the rationale for the selection of its mathematical expression, and calculate the entropy of this source. (6 marks) (b) For each of the codes reported in the table below specify if it is a prefix code and if it is reversible. Motivate your answer. (4 marks) Question 2 continued on page 3... Continuation of Question 2: Source Probability of Code 1 Code 11 Code III Occurrence Symbol SO 0.4 1 1 0 S1 0.2 11 01 11 S2 0.2 000 011 10110 S3 0.15 110 0111 00111 S4 0.05 1100 01111 001111 (c) Derive a Huffman code for the discrete source specified above. (4 marks) (c) Derive a Huffman code for the discrete source specified above. (4 marks) (d) Encode the following sequence emitted by the source with the code derived and provide the output of the encoder: So S1 SO SO S2 SO SO SO S3 SO (3 marks) (e) Assuming the source emits 100 symbols per second, calculate the expected bit rate output by the source encoder when the Huffman code you have derived is used. (3 marks) (Total 20 marks)