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 Rh to the transmitter and/or the receiver. We derive upper and lower bounds on the optimal achievable α-th moment of the estimation error and show that they coincide for small values of α and for high values of Rh. The upper bound relies on a recently proposed channel-coding scheme that effectively conveys Rh 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.