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

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Chapter 7: Physical-layer Key Encoding for Wireless Physical-layer Secret-key Generation (WPSG) with Unequal Security Protection (USP) 101 Now, if x = n, which is the number of bits in the generated codeword as well as the number of bits in the plaintext, and I V ′ K + 1 is even, (1 − p) n+1 2 (I′ V K +1) ≤ ( 1 2 )n (7.16) For very large n, (7.16) becomes n+1 lim (1 − p) 2 (I′ V K +1) ≤ lim ( 1 n→∞ n→∞ 2 )n (7.17) (1 − p) n 2 (I′ V K +1) ≤ ( 1 2 )n (7.18) I V ′ 2 K + 1 ≥ − log 2 (1 − p) (7.19) We can see that, as n increases, the minimal value of I V ′ K + 1 that should be set also increases. If we denote by ⌈− 2 2 ⌉ the smallest integer that is larger than − , log 2 (1−p) log 2 (1−p) the direct consequence of (7.19), when I V ′ K + 1 is constrained to be an even number, will be the condition 7.4.1. In case I V ′ K +1 is odd, we use the prototype in Eq. (7.11) and follow the same reasoning. (1 − p) n+1 2 (I′ n−1 V K +1)+ 2 ≤ ( 1 2 )n (7.20) n+1 lim (1 − p) 2 (I′ n−1 V K +1)+ 2 ≤ lim ( 1 n→∞ n→∞ 2 )n (7.21) (1 − p) n 2 (I′ V K +2) ≤ ( 1 2 )n (7.22) I V ′ 2 K + 1 ≥ − log 2 (1 − p) − 1 (7.23) This results in the condition 7.4.2. Therefore, with the same p, we can set I ′ V K + 1 to be smaller by 1 bit if it is odd, as compared with the even case. In the last section, we have suggested two simple generating matrix prototypes for our physical-layer key encoding for two specific cases, when I V K +1 is even and when it is odd, where I V K is the number of vulnerable key bits. I V K + 1 is related to I K , the number of original key bits needed from the quantizer, by Theorem 7.2. In case I V K + 1 is unknown,
102 Chapter 7: Physical-layer Key Encoding for Wireless Physical-layer Secret-key Generation (WPSG) with Unequal Security Protection (USP) we use Theorem 7.4 to derive I V ′ K + 1 as an equivalent of I V K + 1 from the probability p that the eavesdropper incorrectly estimates a key bit. For example, I V ′ K + 1 is at least 5 when p is 0.25, yielding an asymptotic code rate of 3, as predicted by Theorem 7.3. The next section discusses scalable security, which will be related to the physical-layer key encoding in the end. 7.4 Literature Review of Scalability in Practical Security Domain Scalable security has been previously investigated in [22,27,32,72] using selective encryption schemes. The basic idea of the scheme is to encrypt only some important parts of the scalable data. These works consider several video coding standards, especially MPEG-I, from which scalable video data is used to evaluate their encryption scheme. MPEG encoding of a video sequence requires compression in two dimensions. In the time dimension, a combination of blocked-based motion compensation is applied to remove inter-frame temporal redundancy. In the space dimension, discrete cosine transform (DCT)-based compression is used to remove intra-frame spatial redundancy. After compression, frames are formed by several compressed blocks. Then, a number of frames are grouped together to form a random access unit, called a group of pictures (GOP), so that the video can be viewed either forward or backward. Each GOP has little or no dependence on other GOPs [27]. A GOP consists of three types of frames, which are intracoded frames (I-frames), motion-estimated forward predicted frames (P-frames), and motion-estimated bidirectional predicted frames (B-frames). The encoder of the I-frame uses the same scheme as JPEG encoding of still frames. The I-frame is used as the motion-estimated reference for the P- and B- frames. The P-frame is encoded with reference to the most recently previous I- or P- frame, whereas the B-frame is encoded with reference to both the most recently previous as well as the most immediately succeeding I- or P- frame [27].
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Network Coding and Wireless Physica
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Abstract The general abstraction of
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Contents Abstract i Abstract ii Dec
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vi CONTENTS 5.4 Degree Distribution
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List of Figures 2.1 A basic digital
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x LIST OF FIGURES 5.11 Comparison o
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Part I Motivation, Overview, and In
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Chapter 1: Motivation and Overview
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Chapter 2 Introduction to Digital C
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Chapter 2: Introduction to Digital
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33 The emergence of scalable video
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Chapter 4: Unequal Erasure Protecti
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Page 132 and 133: Bibliography [1] 3GPP, “3GPP; Tec
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Page 138 and 139: BIBLIOGRAPHY 125 [63] S. Jaggi, P.
Page 140: BIBLIOGRAPHY 127 [81] X. Sun, X. Wu
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