A source has an alphabet (a₁, a2, a3, a4} with corresponding probabilities (0.1,

0.2, 0.3, 0.4).

1. Find the entropy of the source.

2. What is the minimum required average code word length to represent this source

for error-free reconstruction?

3. Design a Huffman code for the source and compare the average length of the

Huffman code with the entropy of the source.

4. Design a Huffman code for the second extension of the source (take two letters

at a time). What is the average code word length? What is the average number

of required binary letters per each source output letter?

5. Which is a more efficient coding scheme: the Huffman coding of the original

source or the Huffman coding of the second extension of the source?