## Ubiquitous access to distributed data in large-scale sensor networks through decentralized erasure codes (2005)

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### BibTeX

@MISC{Dimakis05ubiquitousaccess,

author = {Alexandros G. Dimakis and Vinod Prabhakaran and Kannan Ramchandran},

title = {Ubiquitous access to distributed data in large-scale sensor networks through decentralized erasure codes},

year = {2005}

}

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### Abstract

Consider a large-scale wireless sensor network of n nodes, where a fraction k out of n generate data packets of global interest. Assuming that the individual nodes have limited storage and computational capabilities, we address the problem of how to enable ubiquitous access to the distributed data packets. Specifically, we assume that each node can store at most one data packet, and study the problem of diffusing the data so that by querying any k nodes, it is possible to retrieve all the k data packets of interest (with high probability). We introduce a class of erasure codes and show how to solve this problem efficiently in a completely distributed and robust way. Specifically we show that we can efficiently diffuse the data by “prerouting” only O(ln n) packets per data node to randomly selected storage nodes. By using the proposed scheme, the distributed data becomes available “at the fingertips” of a potential data collector located anywhere in the network.

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Citation Context ...l rank it suffices to show that the determinant detG ′ �= 0. There is a close connection between determinants of matrices and graph matchings which for the bipartite case is given by Edmonds’ theorem =-=[21]-=-. A bipartite graph will have a perfect matching (P.M.) if there exists a subset E ′ ⊆ E of its edges so that no two edges in E ′ share a common vertex and all the vertices connect to an edge in E ′ .... |

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Citation Context ...nal packets by asking any k encoded storage nodes. The most common erasure codes are Reed-Solomon which are very widely employed in many applications like computer network distributed storage systems =-=[18]-=-, and redundant disk arrays [3]. Also, LDPC codes and more recently fountain codes [19] were proposed as alternatives with randomized construction and faster encoding and decoding times. See [22] for ... |

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Citation Context ...ce results from the fact that the sources are distributed and the total rate of the code required is equal to the joint entropy rate of the sources. Distributed Source Coding Using Syndromes (DISCUS) =-=[23]-=- is a practical means of achieving this. The data nodes form the syndromes of the data packets they observe under suitable linear codes. These syndromes are treated as the data which the nodes pre-rou... |

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Citation Context ...nd Cougar [20]. Flooding can be pruned by constructing an analog to indexes in the network. An efficient indexing scheme is the Geographic Hash Table (GHT), which maps IDs and nodes to a metric space =-=[26]-=-. These approaches yield different tradeoffs between reliability over network changes, latency and communication cost. Decentralized erasure codes can be used to add storage redundancy in any existing... |

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Citation Context ...erefore we will have n = 4 √ N storage nodes and k = ρ √ N data nodes for some constant ρ < 4. The k data nodes can be placed in the grid randomly or by using some optimized sensor placement strategy =-=[11]-=-. Notice that we only have O( √ N) nodes measuring or storing. The rest are used as relays and perhaps it is more interesting to assume that the k data nodes are duty-cycled to elongate the lifetime o... |

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Citation Context ...tems [18], and redundant disk arrays [3]. Also, LDPC codes and more recently fountain codes [19] were proposed as alternatives with randomized construction and faster encoding and decoding times. See =-=[22]-=- for a practical investigation on using these codes for distributed storage. The key feature of our problem that makes these codes unsuitable is the fact that the data is distributed. We could convert... |

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14 |
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Citation Context ...eless property of digital fountain codes. These connections are made explicit in a subsequent section. C. Connections to Network Coding Decentralized erasure codes can be seen as linear Network codes =-=[13]-=-, [14], [15] on the (random) bipartite graph connecting the data and the storage nodes (where each edge corresponds to one prerouted packet). Network coding is an exciting new paradigm for communicati... |

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Citation Context ...out coordination. The key technical condition we need to prove to establish that decentralized erasure codes will be decodable is that the random bipartite graphs we construct have a perfect matching =-=[1]-=- with high probability. The existence of a perfect matching guarantees that the max flow that can go through the network is sufficient. Our main theoretical contribution is in quantifying how sparse t... |

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Distributed Data Storage in Sensor Networks Using Decentralized Erasure Codes
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Citation Context ...ility. The key issue, of course, is whether it is possible to achieve This research was supported by NSF under grants CCR-0219722 and CCR0330514. This work has been presented in part at Asilomar 2004 =-=[4]-=-. this robust distributed storage under the communication and storage constraints imposed by the nature of wireless sensors. Our main result is a novel scheme for data dissemination that can guarantee... |

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Citation Context ... how sparse these random bipartite graphs can be under these constraints. The proof is obtained by using an extension of a combinatorial counting technique introduced by P. Erdős and A. Rényi in [5], =-=[2]-=- for analyzing matchings in random bipartite graphs. The extension stems from the dependencies on the data nodes which destroy the symmetry assumed in [5], [2] and thereby complicating matters (see Se... |

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Citation Context ...fying how sparse these random bipartite graphs can be under these constraints. The proof is obtained by using an extension of a combinatorial counting technique introduced by P. Erdős and A. Rényi in =-=[5]-=-, [2] for analyzing matchings in random bipartite graphs. The extension stems from the dependencies on the data nodes which destroy the symmetry assumed in [5], [2] and thereby complicating matters (s... |

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Citation Context ...ty of digital fountain codes. These connections are made explicit in a subsequent section. C. Connections to Network Coding Decentralized erasure codes can be seen as linear Network codes [13], [14], =-=[15]-=- on the (random) bipartite graph connecting the data and the storage nodes (where each edge corresponds to one prerouted packet). Network coding is an exciting new paradigm for communication in networ... |

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Citation Context ...networks. This paper investigates some connections between network coding and codes for distributed storage. A related investigation on applications of network coding on random graphs can be found in =-=[7]-=-. An equivalent way of thinking of the distributed storage problem is that of a random bipartite graph connecting the k data nodes with the n storage nodes and then adding a data collector forsevery p... |