The University of Sydney School of Electrical & Information Engineering ELEC5512 Assignment 2 Due: 23:59, Tuesday, November 3, 2020 1. A very simple line code used in the early data networks is called bit stuffing. The objective of this code is to prevent long runs of 1s and 0s but not necessarily achieve DC balance. The encoding works as follows. Suppose the maximum number of consecutive 1s that we are allowed in the bit stream is k. Then the encoder inserts a 0 bit whenever it sees k consecutive 1 bits in the input sequence. (a) Suppose the incoming data to be transmitted is 111111111111111001000001. What is the encoded bit stream, assuming k = 7? (2 Marks) (b) What is the algorithm used by the decoder to recover the data? Suppose that the received bit stream is 01111111010111111100011. What is the decoded bit stream? (3 Marks) 2. Consider the add/drop element shown in the following figure: (a) 1 2 3 λ2 λ2 λ1 λ2 λ3 λ4 λ1 λ3 λ4 λ1 λ3 λ4 Drop (b) λ1 λ2 λ3 λ4 λ1 λ2 λ3 λ4 1 2 3 λ2 λ2 Drop Add Fiber Bragg grating Fiber Bragg grating Coupler Suppose that a 5% tap is used to couple the added signal into the output, and the grating has a loss of 0.5 dB for the transmitted signal and no loss for the reflected 1 signal. Assume that the circulator has a loss of 1 dB per pass. One way to realize an add/drop multiplexer that adds and drops four wavelengths is to cascade four add/drop elements of the type shown in the subfigure (b) in series. In this case, determine: (a) the best-case loss seen by a channel that is dropped, (2 Marks) (b) the worst-case loss seen by a channel that is dropped, (2 Marks) (c) the best-case loss seen by a channel that is added, (2 Marks) (d) the worst-case loss seen by a channel that is added, (2 Marks) (e) the best-case and worst-case loss for a channel that is passed through. (4 Marks) 3. Which sublayer within the SONET or optical layer would be responsible for handling the following functions: (a) A SONET path fails and the traffic must be switched over to another path. (2 Marks) (b) Many SONET streams are to be multiplexed onto a higher-speed stream and transmitted over a SONET link. (2 Marks) (c) The error rate on a SONET link between regenerators is to be monitored. (2 Marks) (d) Setting up and taking down lightpaths in the network. (2 Marks) (e) Rerouting all the lightpaths on a failed link onto another link. (2 Marks) 4. Suppose that you want to connect two SDH boxes operating at STM-16 line rate over a link that can have a loss anywhere from 0 to 7 dB. However, they do not support the same interface. One of them has an I-16 interface and the other supports S-16.1 interface. The specifications of these interfaces are given in the following ta- ble. How can you interconnect these boxes and make the link budget work? You are allowed to use variable optical attenuators in the link. (6 Marks) 2 Parameter I-16 S-16.1 Transmitter MLM SLM Wavelength range 1.3 µm 1.3 µm Transmit power (max) -3 dBm 0 dBm Transmit power (min) -10 dBm -5 dBm Receiver sensitivity (min) -18 dBm -27 dBm Receiver overload -3 dBm 0 dBm Note: receiver overload is defined as the maximum acceptable value of the re- ceived average power for a 1× 10−10 BER. 5. A lightwave communication link, operating at a wavelength of 1.5 µm and a bit rate of 1 Gb/s has a receiver consisting of a cascaded optical amplifier, narrow optical filter, and photodetector. It ideally takes at least 130 photons/bit to achieve 10−15 bit error rate. (a) How many photons per bit would it take to achieve the same error rate at 10 Gb/s? (2 Marks) (b) At this wavelength 1 mW of power is carried by 7.5×1015 photons per second. What is the received power level for 10−15 bit error rate at 1 Gb/s? (Express the answer in dBm). (3 Marks) 6. Consider a device with three ports where it is desired to send all the energy input at ports 1 and 2 to port 3. Assume that all ports can be used as inputs and outputs. The scattering matrix of such a device can be written as S = 0 0 s13 0 0 s23 s31 s32 s33 . Show that a scattering matrix of this form cannot satisfy the conservation of en- ergy condition. Thus it is impossible to build a device that combines all the power from two input ports to a third port, without loss. (6 Marks) 7. Consider a 4×4 crossbar switch. Assume that powers can be added and we do not have to worry about individual electric fields adding in phase. 3 (a) If each 2×2 switch has crosstalk suppression of 50 dB, what is the overall crosstalk suppression of the switch? (3 Marks) (b) What should be the crosstalk suppression of each 2×2 switch if the overall crosstalk suppression is 40 dB. (3 Marks) Note: If a switch has a crosstalk suppression of 50 dB, it means that the input power from each other input is 10−5 of the input power from the desired input. 4
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