hw2.pdf - EE 284 F Tobagi Autumn 2017-2018 EE284 Homework...

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EE 284 F. Tobagi Autumn 2017-2018 EE284 Homework Assignment No. 2 Topics: Physical Layer Handed out: 10 October, 2017 Due: 17 October, 2017 Total Points: 53 ALL WORK MUST BE SHOWN TO RECEIVE FULL CREDIT Problem 1: Encoding Techniques (15 points) Consider the following encoding techniques: 1. Nonreturn to Zero Level (NRZ-L): NRZ-L maintains a constant voltage level for the duration of a bit time (a pulse). A negative voltage is used to represent binary 1 and a positive voltage is used to represent binary 0. 2. Nonreturn to Zero, Invert on Ones (NRZI): As with NRZ-L, NRZI maintains a constant voltage level for the duration of a bit time. The data bits are encoded by means of signal transitions at the beginning of the bit time. A transition (low-to-high or high-to- low) at the beginning of a bit time indicates a binary 1 for that bit time; no transition indicates a binary 0. 3. Bipolar-Alternate Mark Inversion (Bipolar-AMI): A binary 0 is represented by no line signal, and a binary 1 is represented by a positive or negative voltage pulse. The binary 1 pulses must alternate in polarity. 4. Manchester: There is a transition at the middle of each bit period. The mid-bit transi- tion serves as a clocking mechanism and also to encode the data bits. More specifically, a low-to-high transition represents a 1, and a high-to-low transition represents a 0. 5. Differential Manchester: The mid-bit transition is used only to provide clocking. The encoding of a 0 is represented by the presence of a transition at the beginning of a bit period, and a 1 is represented by the absence of a transition at the beginning of a bit period. 1
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Note: NRZI is an example of differential encoding. In differential encoding, the signal is decoded by comparing the polarity of adjacent signal elements rather than determining the absolute value of a signal element. Figure 1 shows the signal resulting from encoding the data sequence 01001100011 accord- ing to the above described encoding techniques. Differential Manchester 0 1 0 0 1 1 0 0 0 1 1 NRZ-L NRZI Bipolar-AMI Manchester Figure 1: Encoding techniques Consider the above described encoding techniques, one at a time, and for each encoding technique, answer the following questions: a) [1 points per encoding technique] Given that we are interested in transmitting data at a rate of W bits/sec, express the required signaling rate in terms of W. b) [0.5 points per encoding technique] Draw the signal resulting from encoding the data sequence: 011011100101. In the case of differential encoding, assume that the signal is at a low level before encoding the first bit of the sequence. c) [0.5 points per encoding technique] Draw the signal resulting from encoding the data sequence consisting of alternating 1’s and 0’s: (10101010. . . ). What is the resulting rate of transition, expressed in terms of W? In the case of differential encoding, assume that the signal is at a low level before encoding the first bit of the sequence.
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