Secret-key Agreement with Channel State Information at the Transmitter

TL;DR

This paper investigates the maximum rate at which a secret key can be generated over a wiretap channel with known channel states at the transmitter, deriving bounds and optimal schemes especially for Gaussian channels with interference.

Contribution

It introduces new bounds on secret-key capacity with noncausal state information and proposes schemes that achieve capacity in special cases, including Gaussian channels.

Findings

Bounds on secret-key capacity derived for channels with state information.

Optimal schemes for Gaussian channels with interference are identified.

Capacity is achieved when the receiver also knows the state sequence.

Abstract

We study the capacity of secret-key agreement over a wiretap channel with state parameters. The transmitter communicates to the legitimate receiver and the eavesdropper over a discrete memoryless wiretap channel with a memoryless state sequence. The transmitter and the legitimate receiver generate a shared secret key, that remains secret from the eavesdropper. No public discussion channel is available. The state sequence is known noncausally to the transmitter. We derive lower and upper bounds on the secret-key capacity. The lower bound involves constructing a common state reconstruction sequence at the legitimate terminals and binning the set of reconstruction sequences to obtain the secret-key. For the special case of Gaussian channels with additive interference (secret-keys from dirty paper channel) our bounds differ by 0.5 bit/symbol and coincide in the high signal-to-noise-ratio and high interference-to-noise-ratio regimes. For the case when the legitimate receiver is also revealed the state sequence, we establish that our lower bound achieves the the secret-key capacity. In addition, for this special case, we also propose another scheme that attains the capacity and requires only causal side information at the transmitter and the receiver.