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.
We formulate a problem of state information transmission over a state-dependent channel with states known at the transmitter. In particular, we solve a problem of minimizing the mean-squared channel state estimation error E spl par S sup n - S spl circ sup n spl par for a state-dependent additive Gaussian channel Y sup n = X sup n + S sup n + Z sup n with an independent and identically distributed (i.i.d.) Gaussian state sequence S sup n = (S sub 1 , ..., S sub n ) known at the transmitter and an unknown i.i.d. additive Gaussian noise Z sup n . We show that a simple technique of direct state amplification (i.e., X sup n = spl alpha S sup n ), where the transmitter uses its entire power budget to amplify the channel state, yields the minimum mean-squared state estimation error. This same channel can also be used to send additional independent information at the expense of a higher channel state estimation error. We characterize the optimal tradeoff between the rate R of the independent information that can be reliably transmitted and the mean-squared state estimation error D. We show that any optimal (R, D) tradeoff pair can be achieved via a simple power-sharing technique, whereby the transmitter power is appropriately allocated between pure information transmission and state amplification.  We consider the problem of rate-R, channel coding with causal noncausal side information at the transmitter, under an additional requirement of minimizing the amount of information that can be learned from the channel output about the state sequence, which is defined in terms of the mutual information between the state sequence and the channel output sequence. A single-letter characterization is provided for the achievable region of pairs (R, E) . Explicit results for the Gaussian case (Costa's dirty-paper channel) are derived in full detail.