Polar Coding for Secure Transmission and Key Agreement
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Date
2010-02-25
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Abstract
Wyner's work on wiretap channels and the recent works on information
theoretic security are based on random codes. Achieving information
theoretical security with practical coding schemes is of definite
interest. In this note, the attempt is to overcome this elusive task
by employing the polar coding technique of Arikan. It is shown that
polar codes achieve non-trivial perfect secrecy rates for binary-input
degraded wiretap channels while enjoying their low encoding-decoding complexity.
In the special case of symmetric main and eavesdropper channels,
this coding technique achieves the secrecy capacity.
Extension of the coding technique to the multiple-access
channels with a degraded eavesdropper is discussed.
Finally, fading erasure wiretap channels are considered and
a secret key agreement scheme is proposed, which requires only the
statistical knowledge of the eavesdropper channel state
information (CSI). The enabling factor is the creation of advantage
over Eve, by blindly using the proposed
scheme over each fading block, which is then exploited with
privacy amplification techniques to generate secret keys.