Stochastic Orders, Alignments, and Ergodic Secrecy Capacity

doi:10.1017/9781316450840.010

9 - Stochastic Orders, Alignments, and Ergodic Secrecy Capacity

from Part II - Secure Communication

Published online by Cambridge University Press: 28 June 2017

P.-H. Lin and

Edited by

Ashish Khisti and

P.-H. Lin: Affiliation:
Chair for Communications Theory, Technische Universität Dresden
E. A. Jorswieck: Affiliation:
Chair for Communications Theory, Technische Universität Dresden
Rafael F. Schaefer: Affiliation:
Technische Universität Berlin
Holger Boche: Affiliation:
Technische Universität München
Ashish Khisti: Affiliation:
University of Toronto
H. Vincent Poor: Affiliation:
Princeton University, New Jersey

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Summary

We investigate the relation between different stochastic orders and the degradedness of a fast fading wiretap channel with statistical channel state information at the transmitter (CSIT). In particular, we derive sufficient conditions to identify the ergodic secrecy capacities for both single and multiple antenna cases even though there is only statistical CSIT.

Introduction

To design a wiretap code with higher secrecy rate, channel state information at the transmitter of the legitimate and eavesdropper's channels1 should be known to a certain degree. When there is perfect CSIT of both channels, the secrecy capacity of a Gaussian wiretap channel can be achieved by a Gaussian input. However, due to several practical issues such as (1) being a malicious user, Eve is by no means intending to feed back the correct CSI to Alice; (2) limited feedback bandwidth; (3) the delay caused by channel estimation; (4) the speed of channel variation, etc., it is more reasonable to consider cases where perfect CSIT is unavailable.

In this chapter we consider the cases when only statistical CSIT of both channels from Alice to Bob and Alice to Eve, respectively, are available. One possible way to get such information from Eve virtually is as follows. For some bounded space like indoor parking lots or malls, it is possible to collect the channel statistics offline of most of the positions within that space, where the channel variation may be due to the movement of people or cars, etc. When Alice wants to transmit, she can use the known statistics measured offline of the channel between her and the unknown user closest to her as Eve's channel information to design her wiretap code for the worst-case scenario.

Although the secrecy capacity formula for discrete memoryless non-degraded wiretap channels was proved in [1], the optimal selection of the auxiliary random variable and channel prefixing are still unknown for additive white Gaussian noise (AWGN) channels with partial CSIT in general. Only a few capacity results under the considered scenario are known, and are summarized as follows.

Type: Chapter
Information: Information Theoretic Security and Privacy of Information Systems , pp. 231 - 257

DOI: https://doi.org/10.1017/9781316450840.010 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2017

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