Determine the bit period tc required for the binary channel

Question

Assignment:

In the following system

• the digital message {x(nT)} is made of iid symbols with period T = 1µs, alphabet Ax = {0, 1, 2,..., 9} and PMD

P_x(0) = P_x(1) = 1/4, P_x(2) = ..,= P_x(9) = 1/16

• the source coding scheme uses a binary prefix code with efficiency η = 1.

• the channel coding uses a (3,2) linear systematic code with generating matrix

G= [1 1^I2]

the binary channel is memoryless and symmetric with Pbit = 1/10

a) Write the source coding map µs(·) and the channel decoding map µd(·).

b) Find the bit period Tc required for the binary channel.

c) Find the probability that P[xˆ(nT) = 1 |x(nT) = 0].