Solve the following problem:
A stationary source generates outputs at a rate of 10,000 samples. The samples are independent and are uniformly distributed on the interval [-4, 4]. Throughout this problem the distortion measure is assumed to be squared-error distortion.
1. If perfect (distortion-free) reconstruction of the source at the destination is required, what is the required transmission rate from the source to the destination?
2. If the transmission rate from the source to the destination is zero, what is the minimum achievable distortion?
3. If a five-level uniform quantizer is designed for this source and the quantizer output is entropy-coded using a Huffman code designed for single-source outputs, what is the resulting transmission rate and distortion?
4. In part 3 if the Huffman code is designed for very large blocks of source outputs rather than single source outputs, what is the resulting transmission rate and distortion?