# Intrinsic Capacity

## TL;DR

This paper investigates the capacity limits of channels with intrinsic states when causal state information is available at the encoder and/or decoder, providing new theoretical insights and specific results for binary channels.

## Contribution

It introduces a framework for analyzing channel capacities with intrinsic states and causal information, including generalizations of key theorems and conditions for the usefulness of state information.

## Key findings

- Maximum and minimum capacities for binary channels are characterized.
- A generalization of the Birkhoff-von Neumann theorem is presented.
- Conditions under which causal state information is useless are identified.

## Abstract

Every channel can be expressed as a convex combination of deterministic channels with each deterministic channel corresponding to one particular intrinsic state. Such convex combinations are in general not unique, each giving rise to a specific intrinsic-state distribution. In this paper we study the maximum and the minimum capacities of a channel when the realization of its intrinsic state is causally available at the encoder and/or the decoder. Several conclusive results are obtained for binary-input channels and binary-output channels. Byproducts of our investigation include a generalization of the Birkhoff-von Neumann theorem and a condition on the uselessness of causal state information at the encoder.