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11 - Super-Activation as a Unique Feature of Secure Communication over Arbitrarily Varying Channels

from Part II - Secure Communication

Published online by Cambridge University Press:  28 June 2017

By
R. F. Schaefer ,
H. Boche  and
H. V. Poor
Edited by
Rafael F. Schaefer ,
Holger Boche ,
Ashish Khisti  and
H. Vincent Poor
R. F. Schaefer
Affiliation:
Information Theory and Applications Chair, Technische Universität Berlin
H. Boche
Affiliation:
Chair of Theoretical Information Technology, Technische Universität München
H. V. Poor
Affiliation:
Department of Electrical Engineering, Princeton University
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

The question of whether the capacity of a channel is additive or not goes back to Shannon, who asked this for the zero-error capacity function. Despite the common sense that the capacity is usually additive, there is surprisingly little known for non-trivial channels. This chapter addresses this question for the arbitrarily varying wiretap channel (AVWC), which models secure communication in the presence of arbitrarily varying channel (AVC) conditions. For orthogonal AVWCs it has been shown that the strongest form of non-additivity occurs: the phenomenon of super-activation. That is, there are orthogonal AVWCs, each having zero secrecy capacity, which allow for transmission with positive rate if they are used together. Subsequently, the single-user AVC is studied and it is shown that in this case, super-activation for non-secure message transmission is not possible, making it a unique feature of secure communication over AVWCs. However, the capacity for message transmission of the single-user AVC is shown to be super-additive, including a complete characterization. Super-activation was known for a long time in the area of quantum communication, where it is common opinion that this is solely a phenomenon of quantum physics and that this cannot occur for classical communication. However, the results in this chapter show that super-activation is indeed a feature of secure communication and therewith occurs in classical, non-quantum, communication as well.

Introduction

Information theory goes back to Shannon's seminal work “A Mathematical Theory of Communication” [1]. Since then it has been proven to be an indispensable concept for analyzing complex communication systems to obtain insights and optimal design criteria. Among many things, it is used to address the important issue of medium access control: How should available resources be divided among multiple users in the best possible way? This is a crucial question, especially for wireless communication systems since they are usually composed of orthogonal sub-systems such as those that arise via time division multiplexing (TDM) or orthogonal frequency division multiplexing (OFDM). Of particular interest then is to know how the capacity of the overall system depends on the orthogonal sub-systems. Common sense tells us that for such systems it should be given by the sum of the capacities of all sub-systems. This goes along with the inherent world view of the additivity of classical resources.

Type
Chapter
Information
Information Theoretic Security and Privacy of Information Systems , pp. 313 - 330
Publisher: Cambridge University Press
Print publication year: 2017

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References

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