Power-limited Modulation-Estimation with a Helper

The problem of transmitting a parameter value over an additive white Gaussian noise (AWGN) channel is considered, where, in addition to the transmitter and the receiver, there is a helper that observes the noise non-causally and provides a description of limited rate
$R_{\mathrm{h}}$
to the transmitter and/or the receiver. We derive upper and lower bounds on the optimal achievable
$\alpha-\mathbf{th}$
moment of the estimation error and show that they coincide for small values of
$\alpha$
and for high values of
$R_{\mathrm{h}}$
. The upper bound relies on a recently proposed channel-coding scheme that effectively conveys
$R_{\mathrm{h}}$
bits essentially error-free and the rest of the rate—over the same AWGN channel without help, with the error-free bits being allocated to the most significant bits of the quantized parameter.