Consider the following 2-user multiple access channel (MAC) Y = X1+X2 where X1 {0,1}, X2 {0,1,2}and + is real addition.

Answer the following questions.

1. Compute the maximum I(X1;Y|X2) and specify under what condition this is achievable.

2. Compute the maximum I(X2;Y|X1) and specify under what condition this is achievable.

3. Fix X1 Bernoulli(1/2), compute the maximum I(X2;Y) and specify under what condition this is achievable.

You need to determine the equivalent channel between X2 and Y and nd its capacity.

4. Fix X2 Uniform(1/3), compute the maximum I(X1;Y) and specify under what condition this is achievable.

You need to determine the equivalent channel between X1 and Y and nd its capacity.

5. Plot the rate region for this MAC