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

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Chapter 2: Introduction to Digital Communication Systems and Networks 7 An encryptor provides security to the transmitted data. In cryptology, there are two types of security, which are theoretical security and practical security. They are based on different philosophies. Theoretical security, on the one hand, is based on theoretical impossibility of ciphers being broken, necessitating mutual knowledge of a secret key between transmitter and receiver. Practical security, on the other hand, is based on practical difficulty of ciphers being broken, i.e., it takes too much time and labor to break them. The questions regarding how these two types of security are implemented will be dealt with in Part III. A channel encoder introduces some redundancy to the input data so that the output is immune to deteriorating effects, such as errors and erasures, from the channel. There are numerous channel codes and several ways to classify them. They can be divided into block codes and convolutional codes, fixed-rate and rateless codes, or linear and non-linear codes. In this thesis, we will consider linear rateless codes called LT-codes in Chapter 5. The purpose of a digital modulator is to map the binary representation after channel encoding into electromagnetic waves that can be transmitted along the channel. The simplest digital modulation is called binary modulation, which maps the binary digit 0 into a waveform s o (t) and the binary digit 1 into s 1 (t). This means each bit is transmitted in a separated waveform. In M-ary modulation (M > 2), however, M = 2 m waveforms s i (t), i = 0, 1, ..., M − 1 are used to represent m bits [30]. The communication channel is the physical medium used for transmission, e.g., the free space in wireless communication. In the design and analysis of digital communication systems, communication channels are represented by channel models, which are mathematical abstractions of these physical entities. We will discuss some channel models in the next section. A digital demodulator, a channel decoder, a decryptor, and a source decoder perform reversed operations of a digital modulator, a channel encoder, an encryptor, and a source encoder, respectively. Their overall purpose is to give the binary sink the data which is as close as possible to that generated by the binary source.
8 Chapter 2: Introduction to Digital Communication Systems and Networks 2.2 Channel Models Since channel models are mathematical abstractions of physical channels, they can be divided into several categories based on two factors, which are the nature of physical channels and the levels of abstraction used. We will discuss four frequently used channel models which suit the purpose of this thesis. 2.2.1 Binary Erasure Channel (BEC) Being proposed in 1955 by Elias [52], binary erasure channels become practical for data networks, especially after the emergence of the Internet. The model offers no possibility of transmission errors. It assumes that the data is either received correctly or not received at all. This assumption can only hold on network level of abstraction, where errors are assumed to be corrected by the data link layer. In reality, erasures may be caused by buffer overflows at intermediate routers, mismatching of packets’ internal check-sum, or packets losing their ways [10]. The model can be illustrated by Fig. 2.3, in which X is the transmitted symbol and Y is the received one. If the erasure probability is p e , the capacity C of the channel is given by [73] C = 1 − p e . (2.1) X 1−p e Y 0 0 p e p e e 1 1−p e 1 Figure 2.3: Binary Erasure Channel
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Page 4 and 5: Abstract The general abstraction of
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Page 10 and 11: List of Figures 2.1 A basic digital
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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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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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