Estimation with a helper who knows the interference

TL;DR

This paper investigates the problem of estimating a signal corrupted by interference with the help of a helper who knows the interference, providing new bounds and characterizations for both causal and noncausal knowledge scenarios.

Contribution

It introduces novel bounds and schemes for interference-aware estimation, including the first characterization of optimal distortion in several regimes and the distinction between causal and noncausal cases.

Findings

Derived the minimum distortion for causal interference knowledge.

Established new lower bounds for noncausal interference scenarios.

Showed causal and noncausal estimation are not equivalent in this setting.

Abstract

We consider the problem of estimating a signal corrupted by independent interference with the assistance of a cost-constrained helper who knows the interference causally or noncausally. When the interference is known causally, we characterize the minimum distortion incurred in estimating the desired signal. In the noncausal case, we present a general achievable scheme for discrete memoryless systems and novel lower bounds on the distortion for the binary and Gaussian settings. Our Gaussian setting coincides with that of assisted interference suppression introduced by Grover and Sahai. Our lower bound for this setting is based on the relation recently established by Verd\'u between divergence and minimum mean squared error. We illustrate with a few examples that this lower bound can improve on those previously developed. Our bounds also allow us to characterize the optimal distortion in several interesting regimes. Moreover, we show that causal and noncausal estimation are not equivalent for this problem. Finally, we consider the case where the desired signal is also available at the helper. We develop new lower bounds for this setting that improve on those previously developed, and characterize the optimal distortion up to a constant multiplicative factor for some regimes of interest.