1. In this problem, under consideration is a convolutional code (referred to as C) whose state...

 

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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 C B 0 +1, +1 C B 1 -1,-1 C 0 +1,-1 C 1 -1, +1 D 0 +1,-1 D 1 -1, +1 A B D D B Assume that the communication channel is AWGN. More precisely speaking, ifs is 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 w is 1/2. (a). (5%) Find E/No, where E, is the code-bit energy, and No/2 is the two-sided power spectral density of the AWGN. In the meantime, please be reminded that №o/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. 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 C B 0 +1, +1 C B 1 -1,-1 C 0 +1,-1 C 1 -1, +1 D 0 +1,-1 D 1 -1, +1 A B D D B Assume that the communication channel is AWGN. More precisely speaking, ifs is 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 w is 1/2. (a). (5%) Find E/No, where E, is the code-bit energy, and No/2 is the two-sided power spectral density of the AWGN. In the meantime, please be reminded that №o/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.

Answer rating: 100% (QA)

a To find EcNo we need to calculate the codebit energy Ec and No2 the twosided power spectral density of the AWGN The variance of the noise No2 is giv... View the full answer