Design a binary huffman code for the source find the

Question

A discrete memory less source produces outputs {a₁, a_2, 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?