Solve the following problem:
A discrete memory less source produces outputs {a1, a2, a3, a4, a5, a6, a7, a8}. The corresponding output probabilities are 0.05, 0.07, 0.08, 0.1, 0.1, 0.15, 0.2, and 0.25.
1. Design a binary Huffman code for the source. Find the average codeword length. Compare it to the minimum possible average codeword length.
2. What is the minimum channel capacity required to transmit this source reliably? Can this source be reliably transmitted via a binary symmetric channel?
3. If a discrete memory less zero-mean Gaussian source with σ2 = 1 is to be transmitted via the channel of part 2, what is the minimum attainable mean squared distortion?