# State Leakage and Coordination with Causal State Knowledge at the Encoder

## TL;DR

This paper analyzes how causal and strictly causal state knowledge at the encoder affects state masking, amplification, and coordination in channels, introducing a new framework for understanding decoder inference and solving a related game.

## Contribution

It characterizes rate-equivocation-coordination regions for state-dependent channels with causal state knowledge and extends to two-sided information and feedback scenarios.

## Key findings

- Characterized trade-offs for state masking and amplification.
- Introduced the notion of core of the receiver's knowledge.
- Solved a channel state estimation zero-sum game.

## Abstract

We revisit the problems of state masking and state amplification through the lens of empirical coordination. Specifically, we characterize the rate-equivocation-coordination trade-offs regions of a state-dependent channel in which the encoder has causal and strictly causal state knowledge. We also extend this characterization to the cases of two-sided state information and noisy channel feedback. Our approach is based on the notion of core of the receiver's knowledge, which we introduce to capture what the decoder can infer about all the signals involved in the model. Finally, we exploit the aforementioned results to solve a channel state estimation zero-sum game in which the encoder prevents the decoder to estimate the channel state accurately.