# On the Capacity for Distributed Index Coding

## TL;DR

This paper advances the understanding of distributed index coding by developing a new coding scheme, establishing capacity bounds, and demonstrating optimality in most small-scale cases.

## Contribution

It introduces a novel distributed composite coding scheme and new outer bounds, solving the sum-capacity for most four-message problems.

## Key findings

- Achieved capacity for 213 out of 218 small-scale problems.
- Enhanced the composite coding scheme for centralized index coding.
- Established new outer bounds on capacity region.

## Abstract

The distributed index coding problem is studied, whereby multiple messages are stored at different servers to be broadcast to receivers with side information. First, the existing composite coding scheme is enhanced for the centralized (single-server) index coding problem, which is then merged with fractional partitioning of servers to yield a new coding scheme for distributed index coding. New outer bounds on the capacity region are also established. For 213 out of 218 non-isomorphic distributed index coding problems with four messages the achievable sum-rate of the proposed distributed composite coding scheme matches the outer bound, thus establishing the sum-capacity for these problems.