12.2-4 Consider a 1nessage source that generates one of fot1r messages randomJy every microseco11d. The probabilities of these messages are 0.4, 0.3, 0.2, and 0.1, respective1y. Each emitted message is independent of the other messages in the sequence. (a) Obtain the compact binary code, and find the average length of the codeword. Determine the efficie11cy a11d the redundancy of this code. (b) If two consecutive messages are encoded jointly, obtain the compact binary code, and find the average length in the codeword. Determine the efficiency and the redundancy of this code