Estimating parameters with limited coded side information improves accuracy
Estimation with Quantized Parameter Side-Information
Information Theory
Summary
Estimating unknown quantities often uses measurements, but sometimes extra clues about those quantities are only given in a simplified form with limited detail. This paper looks at how well one can estimate when they get both standard observations and a simplified, limited version of the actual parameter, where the simplification can be chosen but has a limited number of levels. The authors find mathematical limits on how accurately the parameter can be estimated in this scenario. They show their upper and lower error bounds behave similarly when more data and more detail in the simplified clues are available.
What this means in practice
- •For network signal engineers: Design signal receivers that combine raw data with optimized simplified metadata to reduce estimation error in noisy communication channels.
- •For sensor system designers: Improve parameter inference in sensor networks where sensors send compressed versions of local parameters alongside measurements for better overall accuracy.
Authors
Mathis Wetterwald, Ofer Shayevitz, Michèle Wigger
Abstract
This paper presents upper and lower bounds on the minimax risk of a parameter estimation problem where the estimator not only observes independent and identically distributed observations but also a quantized version of the parameter, where the quantization has a limitation on the number of levels, but can be optimized otherwise. Our upper and lower bounds have similar decay rates for large number of observation samples and quantization levels.