Solve the following problem:
The optimum four-level non uniform quantizer for a Gaussian-distributed signal amplitude results in the four levels a1, a2, a3, and a4, with corresponding probabilities of occurrence p1 = p2 = 0.3365 and p3 = p4 = 0.1635.
1. Design a Huffman code that encodes a single level at a time, and determine the average bit rate.
2. Design a Huffman code that encodes two output levels at a time, and determine the average bit rate.
3. What is the minimum rate obtained by encoding J output levels at a time as J → ∞?