Solve the following problem:
A binary memory less source generates 0 and 1 with probabilities 1/3 and 2/3, respectively. This source is to be transmitted over an AWGN channel using binary PSK modulation.
1. What is the absolute minimum Eb/N0 required to be able to transmit the source reliably, assuming that hard decision decoding is employed by the channel and for each source output you can use one channel transmission.
2. Under the same conditions as in part 1, find the minimum Eb/N0 required for reliable transmission of the source if we can transmit at a rate at most equal to the cutoff rate of the channel.
3. Now assume the source is a zero-mean memory less Gaussian source with variance