Response to the following problem:
A discrete memory less source produces outputs {a1, a2, a3, a4, a5}. The corresponding output probabilities are 0.8, 0.1, 0.05, 0.04, and 0.01.
1. Design a binary Huffman code for the source. Find the average codeword length. Compare it to the minimum possible average codeword length.
2. Assume that we have a binary symmetric channel with crossover probability ε = 0.3. Is it possible to transmit the source reliably over the channel? Why?
3. Is it possible to transmit the source over the channel employing Huffman code designed for single source outputs?