1. Consider an alphabet of a discrete memoryless source having six source symbols with their...

1. Consider an alphabet of a discrete memoryless source having six source symbols with their respective probabilities as 0.08, 0.10, 0.12, 0.15, 0.25, and 0.30. Create a binary Huffman tree and determine the codeword for each symbol.

2. For the Huffman codeword determined in Example 5.2.13, determine the minimum possible average codeword length attainable by coding an infi nitely long sequence of symbols.

3. Compute the average length of the Huffman source code determined in Example 5.2.13. Also show that the code effi ciency is 98.7%.

4. For a third-order extension, the binary Huffman source code for a discrete memoryless source generates two symbols with probability 0.8 and 0.2 respectively. How many possible messages are available? Find the probabilities of all new message symbols.