Trade-offs Between Weak-Noise Estimation Performance and Outage Exponents in Nonlinear Modulation

TL;DR

This paper investigates the fundamental trade-offs in nonlinear modulation systems between estimation accuracy under weak noise and the probability of outage errors, providing bounds and a lattice code scheme that achieves optimality at high SNR.

Contribution

It introduces a novel approach to separate and analyze weak-noise and outage errors, deriving bounds on their trade-off and proposing a lattice coding scheme that attains these bounds at high SNR.

Findings

Bounds on the trade-off between weak-noise error decay and outage probability decay.

Lattice codes can achieve the optimal trade-off at high SNR.

The approach clarifies the impact of system design choices on estimation performance and outage risk.

Abstract

We focus on the problem of modulating a parameter onto a power-limited signal transmitted over a discrete-time Gaussian channel and estimating this parameter at the receiver. Considering the well-known threshold effect in non-linear modulation systems, our approach is the following: instead of deriving upper and lower bounds on the total estimation error, which weigh both weak-noise errors and anomalous errors beyond the threshold, we separate the two kinds of errors. In particular, we derive upper and lower bounds on the best achievable trade-off between the exponential decay rate of the weak-noise expected error cost and the exponential decay rate of the probability of the anomalous error event, also referred to as the outage event. This outage event is left to be defined as part of the communication system design problem. Our achievability scheme, which is based on lattice codes, meets the lower bound at the high signal-to-noise (SNR) limit and for a certain range of trade-offs between the weak--noise error cost and the outage exponent.