State amplification under masking constraints

This paper considers a state dependent channel with one transmitter, Alice, and two receivers, Bob and Eve. The problem at hand is to effectively "amplify" the channel state sequence at Bob while "masking" it from Eve. The extent to which the state sequence cannot be masked from Eve is referred to as leakage, and the paper is aimed at characterizing the tradeoff-region between amplification and leakage rates for such a system. An achievable coding scheme is presented, wherein the transmitter enumerates the state sequence using two indices, and transmits one of the indices over the channel to facilitate the amplification process. For the case when Bob observes a "stronger" channel than Eve, the achievable coding scheme is enhanced with secure refinement. The optimal amplification-leakage rate difference, called as differential amplification capacity, is characterized for the degraded binary and the degraded Gaussian channels. For the degraded Gaussian model, extremal corner points of the trade-off region are characterized. In addition, the gap between the outer bound and achievable rate-regions is determined, where it is shown that the gap is less than half a bit for a wide set of channel parameters.