Finding Sparse Solutions for the Index Coding Problem

Abstract

The Index Coding problem has recently attracted a significant attention from the research community. In this problem, a server needs to deliver data to a set of wireless clients over the broadcast channel. Each client requires one or more packets, but it might have access to the packets requested by other clients as side information. The goal is to deliver the required data to each client with minimum number of transmissions.In this paper, we focus on finding sparse solutions to the Index Coding problem. In a sparse solution each transmitted packet is a linear combination of at most two original packets. We focus both on scalar and vector versions of the problem. For the scalar case, we present a polynomial time algorithm that achieves an approximation ratio of 2 − 1 √ n . For the vector case, we present a polynomial time algorithm that identifies an optimal solution to the problem. Our simulation studies demonstrate that our algorithms achieve good performance in practical scenarios.

The Index Coding problem: A game-theoretical perspective

“…The proof of Lemma 3 uses the reduction from the cycle packing problem and follows the same lines as the complexity proof in [13]. The details are omitted due to the space constraints.…”

“…We denote by Γ = [g i ] the encoding matrix whose rows correspond to encoding vectors of the packets transmitted over the channel. A sparse code [13] is the linear code in which each transmitted packet from the server is a linear combination of at most two packets in P . Without loss of generality, we assume that the cost of transmitting a packet by the server is equal to one, hence the total cost incurred by the server is equal to η.…”

CodHoop: A system for optimizing big data processing

“…• Two link-level packet transmissions to fetch packet P 4 from mapper 2 residing on node 2 , • Four link-level packet transmissions to fetch packet P 8 from mapper 3 residing on node 3 ,…”

“…Our coding scheme for Hadoop MapReduce borrows from novel concepts of the index coding, where each client Wants some information and has some side information [8]. The output of the mapper residing on the same node with a reducer is essentially the reducer's side information, whereas the keys that a specific reducer is assigned to process is what it Wants.…”

“…It has been shown that mixing techniques such as network coding and index coding can significantly increase the rate of information transfer in a network [7], [8], [9], [10], [8]. We therefore propose a novel index coding based algorithm to improve the rate of information transfer during the Hadoop shuffle phase.…”