3. Consider the convolutional encoder of Figure 3a. (a) Using the state diagram of Figure 3b, find the output codeword c for the message sequence d = (101) followed by 2 zeros to flush the register. (b) Assuming that a 5-bit message sequence (followed by zeros) is transmitted. Using the state diagram, find the message sequence when the received sequence r = (110100100110110000...) (c) Consider that the encoder of Figure 3a is used over a binary symmetric channel (BSC). Assume the initial encoder state is the 00 state. At the output of the BSC, the received sequence is r = (1100000111 rest all 0). Find the maximum likelihood path through the trellis diagram and determine the first 5 decoded data bits. Input Figure 3a Output