Index coding problem with side information repositories

To tackle the expected enormous increase in mobile video traffic in cellular networks, an architecture involving base station along with caching femto stations (referred to as helpers), storing popular files near users, has been proposed [1]. The primary benefit of caching is the enormous increase in downloading rate when a popular file is available at helpers near a user requesting that file. In this work, we explore a secondary benefit of caching in this architecture through the lens of index coding. We assume a system with n users and k caching helpers. Only helpers store files i.e., have side information. We investigate the following scenario: Each user requests for a distinct file that is not found in its set of neighboring helpers. Users are served coded packets (through an index code) by an omniscient base station. Every user decodes the desired packet from the coded packets and the side information from helpers nearby. We assume that users can obtain any file stored in their neighboring helpers without incurring transmission costs. With respect to the index code employed, we investigate an achievable scheme based on graph coloring (referred to as XOR coloring). We show that the general problem reduces to a canonical problem where every user is connected to exactly one helper. For the canonical problem, with constant number of helpers (k), we show that the complexity of computing the best XOR coloring scheme is polynomial in the number of users n. The result exploits a special complete bi-partite structure that the side information graphs exhibit for any finite k.