本篇論文檢查了離散無記憶竊聽通道(discrete memoryless wiretap channel)的保密容量，該通道在傳輸者（愛麗絲Alice）處具有非因果性邊訊息(non-causal side information)，並且源頭和目的地（鮑勃Bob）都知道共享密鑰(secret key)，但此密鑰隱藏在竊聽者(夏娃Eve)之外。擬議的可實現方案利用蓋爾芬德–平斯克(Gelfand-Pinsker)編碼來利用邊訊息，並使用向農(Shannon)的一次性碼本(One-time pad)和懷納(Wyner)的竊聽編碼(wiretap coding)來確保對竊聽者的機密性。特別地，需要分箱技術以確保始終可以找到代碼字以與邊訊息匹配並且向竊聽者提供足夠的混淆。在這論文中也展示了保密容量的上限。最後，討論擴展到高斯(Gaussian)情況，其中可實現的速率是通過將德科斯塔(Costa)的髒紙編碼技術(dirty paper coding)應用於竊聽通道場景而得出的。

This work examines the secrecy capacity of a discrete memoryless wiretap channel with non-causal side information at the source (Alice) and a shared secret key that is known by both the source and the destination (Bob), but concealed against the eavesdropper (Eve). The proposed achievable scheme utilizes Gel'fand-Pinsker coding to exploit side information, and Shannon's one-time pad and Wyner's wiretap coding to ensure confidentiality against Eve. In particular, binning techniques are required to ensure that a codeword can always be found to match with the side information and that sufficient confusion is provided to Eve. A converse upper bound of the secrecy capacity is also shown in this work. Finally, the discussions are extended to the Gaussian case, where the achievable rates are derived by applying Costa's dirty paper coding techniques to the wiretap channel scenario.

Abstract i
Contents ii
1 Introduction 1
2 Review of Binning Techniques in Classical Problems 5
2.1 Wyner's Wiretap Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Gel'fand-Pinsker Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Wiretap Channel with Shared Secret Key and Side Information at the
Transmitter 17
3.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 The Lower Bound and the Upper Bound of the Secrecy Capacity . . . . . . . 19
3.3 Achievability Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.3.1 Scenario of Category MS . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.3.2 Scenario of Category MZ . . . . . . . . . . . . . . . . . . . . . . . . . 29
3.3.3 Scenario of Category R . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3.4 Performance Comparison . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.4 Converse Proof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.5 Achievability Proof for Special Cases . . . . . . . . . . . . . . . . . . . . . . 50
3.5.1 Case 1: I(U;Y)≧I(U;Z) and I(U;S)≧I(U;Z) . . . . . . . . . . 50
3.5.2 Case 2: I(U;Y)≧I(U;Z) and I(U;Z)>I(U;S) . . . . . . . . . . 52
3.5.3 Case 3: I(U;Y)4 Gaussian Wiretap Channel with Shared Secret Key and Side Information
at the Transmitter 60
4.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2 Modes of Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.1 GMS-GP Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.2 GMZ-GP Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.2.3 GMZ-WTCK Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.2.4 GR-OTP Mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4.3 Leakage Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4 Mode Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.5 An Achievable Rate With Asymptotic Perfect Secrecy . . . . . . . . . . . . . 79
4.6 Bounds On the Rates With Asymptotic Perfect Secrecy . . . . . . . . . . . . 85
4.6.1 Upper and Lower Bounds . . . . . . . . . . . . . . . . . . . . . . . . 85
4.6.2 Performance Comparison . . . . . . . . . . . . . . . . . . . . . . . . . 85
5 Conclusion 90

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