# Capacity Region of the Symmetric Injective K-User Deterministic Interference Channel

## TL;DR

This paper precisely characterizes the capacity region of the symmetric injective K-user deterministic interference channel by simplifying the Han-Kobayashi scheme and providing tight converses for each facet.

## Contribution

It introduces a simplified capacity region characterization for the symmetric injective K-user DIC by projecting the Han-Kobayashi region and establishing tight bounds.

## Key findings

- The capacity region is fully characterized for all channel parameters.
- The projected region simplifies the analysis by focusing on facets with equal coefficients.
- A tight converse is established for each facet of the simplified region.

## Abstract

We characterize the capacity region of the symmetric injective K-user Deterministic Interference Channel (DIC) for all channel parameters. The achievable rate region is derived by first projecting the achievable rate region of Han-Kobayashi (HK) scheme, which is in terms of common and private rates for each user, along the direction of aggregate rates for each user (i.e., the sum of common and private rates). We then show that the projected region is characterized by only the projection of those facets in the HK region for which the coefficient of common rate and private rate are the same for all users, hence simplifying the region. Furthermore, we derive a tight converse for each facet of the simplified achievable rate region.