Packet-centric approach to distributed sparse-graph coding in wireless ad hoc networks

Abstract

In this paper we present a packet-centric approach for distributed coding in decentralized wireless ad hoc networks, for applications in distributed data storage, data persistence and efficient data gathering. We study the setting where each of N network nodes generates an information packet and the goal is to efficiently encode information packets and disseminate produced encoded packets across the network in such fashion that gathering of any subset of slightly more than N encoded packets allows for retrieval of the original information. The process of distributed encoding is performed using packets that randomly walk over the network and sample information packets from network nodes, producing the encoded packets in a simple, elegant, fully decentralized and stateless way. The proposed scheme maintains properties of centralized codes in terms of performance parameters, offering at the same time advantage of robustness to node failures and changes in network topology. We specialize the proposed scheme for several important classes of low-complexity encodable/decodable sparse-graph codes – LDGM, LDPC (IRA), LT, and Raptor codes, evaluating its performance via simulation for various data-gathering scenarios.

Introduction

Recent advances in coding theory introduced a number of novel coding schemes, advantageous both in performance and complexity, and suitable for a diverse set of potential applications [1]. Among these, sparse-graph codes, such as Low-Density Parity-Check (LDPC) codes [2] and rateless codes [3], gained a particular attention due to their efficiency and simplicity of encoding/decoding algorithms. However, sparse-graph codes have been mainly studied in a centralized network scenario, where the message to be encoded is entirely available at a single network node in charge of the execution of the encoding algorithm. The encoding node produces a codeword by combining the elements of the original message according to the constraints imposed by the code graph.

In contrast to this typical setup, we are interested in the case where message to be encoded is distributed among all network nodes. Each network node is in possession of an equal amount of the original information, i.e., each node generates an information packet that is a fraction of the network message. Our goal is to design an efficient distributed encoding algorithm that will produce a network codeword, consisting of encoded packets dispersed among the network nodes, where the properties of the network codeword should closely match the properties of a codeword encoded in a centralized way. The encoding algorithm should allow for decentralized creation of the code graph that follows the predefined code constraints, while using only local knowledge of the network topology. The potential applications of such an encoding scheme lie in distributed data storage, data persistence and/or efficient data gathering in decentralized wireless ad hoc networks.

The problem of distributed coding with the purpose of distributed data storage and data collection in decentralized environments has drawn a lot of interest lately. Particularly, regarding distributed implementation of sparse-graph codes, several distributed LDPC and rateless coding schemes have been proposed so far [4], [5], [6], [7], [8], [9], addressing different aspects of the problem, assuming various underlying network architectures and devising diverse encoding algorithms. However, the unifying property of all these algorithms is that they are all node-centric, in the sense that all information that controls the execution of the encoding algorithm is maintained by network nodes. Apart from costly communication requirements and often involved implementation, the major drawback of these schemes lies in the fact that failure of network nodes during the encoding process may significantly alter the designed coding constraints, which in turn affects performance of the schemes. In comparison with node-centric methods, our encoding solution achieves required performance with a simpler encoding algorithm.

We propose the packet-centric approach for distributed encoding of sparse-graph codes. The principal idea is to perform control of the encoding process using the information contained within the packets that traverse the network and this is the key difference to all the other schemes proposed so far. These packets, that we refer to as encoded packets, randomly walk over the network, sample and encode information from network nodes, finishing their walks in random network nodes. We derive the general form of the encoding algorithm and investigate impacts of different model assumptions such as network graph models, sparse-graph code schemes, and data gathering strategies on its performance. In particular, the contributions of this paper are: (i) introduction of the general framework for distributed encoding of sparse-graph codes, (ii) investigation of different random walk design algorithms and their impacts on the performance of the distributed encoding, (iii) consideration of realistic wireless ad hoc network random graph models, (iv) performance evaluation of different data gathering strategies and, (v) side-by-side comparison of distributed versions of popular sparse-graph coding solutions derived from the proposed framework.

The organization of the rest of the paper is as follows: Section 2 reviews the related work. In Section 3, the system model assumptions underlying the proposed distributed coding framework are given and potential applications of distributed coding are discussed. Section 4 provides the background on network graph models and random walks on graphs, focusing on the results applicable to the scenario of interest. Section 5 describes the proposed scheme in detail, specializing it for several important classes of low encoding/decoding complexity sparse-graph codes. Section 6 gives simulation results, evaluating the performance of the proposed approach. Finally, Section 7 concludes the paper.