Gaussian State Amplification with Noisy State Observations

TL;DR

This paper investigates how to transmit messages and amplify Gaussian states over a noisy channel when the sender has imperfect knowledge of the state, providing bounds and a novel coding scheme combining analog signaling and Gelfand-Pinsker coding.

Contribution

It introduces new inner and outer bounds for the rate--state-distortion region and a coding scheme that blends analog signaling with a modified Gelfand-Pinsker approach.

Findings

Derived bounds for the rate--state-distortion region.

Proposed a coding scheme combining analog signaling and Gelfand-Pinsker coding.

Analyzed the impact of imperfect state knowledge on transmission and amplification.

Abstract

The problem of simultaneous message transmission and state amplification in a Gaussian channel with additive Gaussian state is studied when the sender has imperfect noncausal knowledge of the state sequence. Inner and outer bounds to the rate--state-distortion region are provided. The coding scheme underlying the inner bound combines analog signaling and Gelfand-Pinsker coding, where the latter deviates from the operating point of Costa's dirty paper coding.