1. In this problem, under consideration is a convolutional code (referred to as C) whose state transition table (STT) is given below: State Input Output NextState A 0 +1, +1 A A 1 -1,-1 B 0 +1, +1 B 1 -1,-1 A 0 +1,-1 B 1 -1.+1 D D 0 +1.-1 D D 1 -1.+1 B Assume that the communication channel is AWGN. More precisely speaking, if sis trans- mitted into the channel, then the received signal is r = s+w, where w is a zero-mean Gaussian noise. In this problem, s is either +1 or -1. Moreover, let us assume that the variance of wis 1/2. (a). (5%) Find E./No, where E, is the code-bit energy, and N./2 is the two-sided power spectral density of the AWGN. In the meantime, please be reminded that N./2 is equal to the variance of w. (b). (5%) Continued from the preceding subproblem, please find E/No, where E, is the message-bit energy. (c). (5%) Does C perform systematic encoding ? (d). (5%) Plot the state transition diagram of C. (e). (5%) Plot three stages of trellis diagram of C. Please do not assume any particular trellis initialization or trellis termination. In other words, the trellis begins at all states, and ends at all states.