Optical Networks - _Problems3_54

Optical Networks - _Problems3_54 - 280 Modulation and...

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280 Modulation and Demodulation techniques have been applied to calculate the capacity limits of optical systems in [MS00]. The principles of signal detection are covered in the classic books by van Trees [vT68] and Wozencraft and Jacobs [WJ90]. For a derivation of shot noise statistics, see [Pap91]. The noise introduced by optical amplifiers has been studied extensively in the literature. Amplifier noise statistics have been derived using quantum mechani- cal approaches [Per73, Yam80, MYK82, Dan95] as well as semiclassical approaches [Ols89, RH90]. There was a great deal of effort devoted to realizing coherent re- ceivers in the 1980s, but the advent of optical amplifiers in the late 1980s and early 1990s provided a simpler alternative. See [BL90, KBW96] for a detailed treatment of coherent receivers. Equalization is treated extensively in many books on digital communication; see, for example, [LM93, Pro00]. The field of error-correcting codes has developed rapidly since its founding by Hamming [Ham50] and Shannon [Sha48] more than a half-century ago. There are many textbooks on this topic; see, for example, [McE77, LC82]. A discussion of FEC techniques in submarine transmission systems appears in [Sab01]. Problems 4.1 A very simple line code used in early data networks is called bit stuffing. The objective of this code is to prevent long runs of 1s or 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 11111111111001000000 (read left to right). What is the encoded bit stream, assuming k = 5 ? (b) What is the algorithm used by the decoder to recover the data? Suppose the received bit stream is 0111110101111100011 (read left to right). What is the decoded bit stream? 4.2 The SONET standard uses scrambling to prevent long runs of 1s and 0s from occurring in the transmitted bit stream. The scrambling is accomplished by a carefully designed feedback shift register shown in Figure 4.13. The shift register consists of flip-flops whose operation is controlled by a clock running at the bit rate and is reset at the beginning of each frame. (a) Suppose the incoming data to be transmitted is 11111111111001000000 .As- sume that the shift register contents are 1111111 at the beginning. What is the scrambled output? (b) Write a simulation program to compute the scrambled output as a function of the input. The input is a sequence of bits generated by a pseudo-random
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Problems 281 sequence with equal probabilities for a 1 and a 0. Plot the longest run length
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Optical Networks - _Problems3_54 - 280 Modulation and...

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