## (solution) Consider the following information bit sequence { b k }= {1011000111}. Draw the NRZI waveform by

Consider the following information bit sequence { b k }= {1011000111}. Draw the NRZI waveform by applying the rule that b k = 1 means there is a level transition while b k = 0 means no transition. Assume that the initial condition is − V volts. Determine the output of the differential encoder, { d k } and again draw the out- put waveform of the NRZ-L modulator. Compare with (a). Assume the initial condition d − 1 = 0. Suppose a polarity reversal occurred after the fourth bit, i.e., at t = 4 T b where transmission starts at 0. Draw the received waveform. Assume that there is no AWGN during transmission. What would the detected differential bits d ˆ k be? Keep in mind d k bits are NRZ-L modulated. What is the detected information sequence, { b ˆ k }? As at the transmitter, the receiver assumes an initial condition of d ˆ − 1 = 0. Suppose that the receiver misunderstands the transmitter and that it assumes an initial condition of d ˆ − 1 = 1. What is the detected information bit sequence now? Finally assume that the technologist realized at t = 7 T b that there was a polarity reversal and corrected it. Draw the received waveform now and determine the detected differential bit sequence, { d ˆ k } and the decoded information bit sequence, { b ˆ k }. Assume d ˆ − 1 = 0 (same as the transmitter). Draw conclusions as to the influence of polarity reversals on the bit error probability.

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Sep 13, 2020

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