# Subspace-Aware Index Codes

## TL;DR

This paper introduces subspace-aware index coding, leveraging low-dimensional data structures to significantly improve system throughput, with an efficient algorithm for near-optimal coding, outperforming traditional methods.

## Contribution

It generalizes index coding to exploit data subspace structures and proposes an efficient alternating minimization algorithm for near-optimal codes.

## Key findings

- Achieves up to 90% throughput gain with subspace-aware codes.
- Develops an algebraic framework for subspace-aware index coding.
- Provides an efficient algorithm for near-optimal code design.

## Abstract

In this paper, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications, the data to be transmitted may lie (or can be well approximated) in a low-dimensional subspace. We exploit this low-dimensional structure of the data using an algebraic framework to solve the index coding problem (referred to as subspace-aware index coding) as opposed to the traditional index coding problem which is subspace-unaware. Also, we propose an efficient algorithm based on the alternating minimization approach to obtain near optimal index codes for both subspace-aware and -unaware cases. Our simulations indicate that under certain conditions, a significant throughput gain (about 90%) can be achieved by subspace-aware index codes over conventional subspace-unaware index codes.