Subspace-Aware Index Codes

Bhavya Kailkhura, Lakshmi Narasimhan Theagarajan, Pramod K. Varshney

Abstract: In this letter, we generalize the well-known index coding problem to exploit the structure in the source-data to improve system throughput. In many applications (e.g., multimedia), 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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">subspace-aware index coding</i> ) as opposed to the traditional index coding problem which is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">subspace-unaware</i> . 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.