Network Coding and Wireless Physical-layer ... - Jacobs University

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Chapter 2: Introduction to Digital Communication Systems and Networks 9 2.2.2 Binary Symmetric Channel (BSC) This model only allows received symbols to contain errors, but not to be erased. However, the physical phenomena behind the transmission errors are not included in the model. Therefore, this model is suitable for the data link level of abstraction. It can be illustrated by Fig. 2.4, in which X is the transmitted symbol and Y is the received one. If the error probability is p s , the capacity C of the channel is given by [73] C = 1 − H(p s ), (2.2) where H(p s ) = p s log 2 1 p s + (1 − p s ) log 2 1 1 − p s , (2.3) 0 1 X 1−p s p s 1−p s p s Y 0 1 Figure 2.4: Binary Symmetric Channel 2.2.3 Additive White Gaussian Noise (AWGN) Channel This channel model, belonging to the physical level of abstraction, explains the transmitted signal distortion as an adding effect of some noise n(t), as follows. r(t) = s(t) + n(t), (2.4) where r(t) is the received signal at time t, s(t) is the transmitted signal, and n(t) is the noise which obeys the following Gaussian distribution. p n (x) = 1 √ 2πσ exp {−(x − m x ) 2 /2σ 2 }, (2.5)
10 Chapter 2: Introduction to Digital Communication Systems and Networks where m x is the mean of the distribution, which is zero in this case, and σ 2 is the noise variance. The assumption of a Gaussian distribution is supported by the natural phenomenon of thermal agitation of charge carriers inside an electrical conductor. The amplitude is almost Gaussian distributed, and the frequency spectrum is almost white, thus the name additive white Gaussian noise (AWGN) [30]. 2.2.4 Rayleigh Fading Channel The Rayleigh fading channel model is a physical abstraction of wireless channels, where signal rays from the transmitter are scattered by obstacles in the environment, forming a number of transmission paths to the receiver, who receives the summation of signals from these paths. Therefore, the received band-pass signal may be expressed as follows [30]. r(t) = ∑ n α n (t)s[t − τ n (t)], (2.6) where α n (t) is the attenuation factor for the signal received on the n th path and τ n (t) is the propagation delay of the n th path. Now, if the transmitted signal s(t) is expressed as s(t) = R[s l (t)e j2πfct ], (2.7) where s l (t) is the low-pass transmitted signal in complex base-band representation and f c is the carrier frequency. The received low-pass signal in base-band can be written as r l (t) = ∑ n α n (t)e −j2πf cτ n (t) s l [t − τ n (t)]. (2.8) According to (2.8), the equivalent low-pass channel in base-band can be described by the following time-variant channel impulse response c(τ; t) = ∑ n α n (t)e −j2πf cτ n (t) δ[t − τ n (t)]. (2.9)
Page 1: Network Coding and Wireless Physica
Page 4 and 5: Abstract The general abstraction of
Page 6 and 7: Contents Abstract i Abstract ii Dec
Page 8 and 9: vi CONTENTS 5.4 Degree Distribution
Page 10 and 11: List of Figures 2.1 A basic digital
Page 12 and 13: x LIST OF FIGURES 5.11 Comparison o
Page 14 and 15: Part I Motivation, Overview, and In
Page 16 and 17: Chapter 1: Motivation and Overview
Page 18 and 19: Chapter 2 Introduction to Digital C
Page 20 and 21: Chapter 2: Introduction to Digital
Page 30 and 31: Chapter 3: Introduction to Graphs a
Page 46 and 47: 33 The emergence of scalable video
Page 48 and 49: Chapter 4: Unequal Erasure Protecti
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Chapter 5: Network Coding with LT C
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Part III Wireless Physical-layer Se
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Chapter 6 Wireless Physical-layer S
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Chapter 6: Wireless Physical-layer
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Chapter 7 Physical-layer Key Encodi
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Chapter 7: Physical-layer Key Encod
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Chapter 8: Summary, Conclusion, and
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Bibliography [1] 3GPP, “3GPP; Tec
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BIBLIOGRAPHY 121 [21] F.A. Hayek,
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BIBLIOGRAPHY 123 [43] M. Friedman a
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BIBLIOGRAPHY 125 [63] S. Jaggi, P.
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BIBLIOGRAPHY 127 [81] X. Sun, X. Wu
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