Determine the message efficiency

Question

Assignment:

A digital message x(nT ) with T = 1µs, has iid symbols with PMD

P_x(1) = P_x(-1) = 1/3, P_x(2) = P_x(-2) = P_x(0) = 1/9

a) Find the message efficiency.

b) Find a source coding scheme in which the output message yn has a ternary alphabet and unit efficiency. What is the symbol period for yn?

c) Is it possible to find a channel coding scheme for yn that will allow transmission over a BSC with symbol period Tb = 400 ns and bit error probability P_bit = 10-2, with an overall error probability P[y_n ≠ y_n] < 10^-7 ?