State Amplification Subject To Masking Constraints

TL;DR

This paper investigates how to effectively amplify channel state information to a legitimate receiver while minimizing leakage to an eavesdropper, characterizing the trade-offs and optimal rates for various channel models.

Contribution

It introduces a new coding scheme for state amplification with masking constraints and derives bounds for the trade-off region, including optimal rates for specific channels.

Findings

Optimal amplification-leakage rate difference characterized for certain channels

Achievable schemes with secure refinement when Bob's signal is stronger

Outer bounds closely approximate the achievable region, within half a bit for Gaussian channels

Abstract

This paper considers a state dependent broadcast channel with one transmitter, Alice, and two receivers, Bob and Eve. The problem is to effectively convey ("amplify") the channel state sequence to Bob while "masking" it from Eve. The extent to which the state sequence cannot be masked from Eve is referred to as leakage. This can be viewed as a secrecy problem, where we desire that the channel state itself be minimally leaked to Eve while being communicated to Bob. The paper is aimed at characterizing the trade-off region between amplification and leakage rates for such a system. An achievable coding scheme is presented, wherein the transmitter transmits a partial state information over the channel to facilitate the amplification process. For the case when Bob observes a stronger signal than Eve, the achievable coding scheme is enhanced with secure refinement. Outer bounds on the trade-off region are also derived, and used in characterizing some special case results. In particular, the optimal amplification-leakage rate difference, called as differential amplification capacity, is characterized for the reversely degraded discrete memoryless channel, the degraded binary, and the degraded Gaussian channels. In addition, for the degraded Gaussian model, the extremal corner points of the trade-off region are characterized, and the gap between the outer bound and achievable rate-regions is shown to be less than half a bit for a wide set of channel parameters.