Abstract—In distributed storage systems that use coding, the issue of minimizing the communication required to rebuild a storage node after a failure arises. We consider the problem of repairing an erased node in a distributed storage system that uses an EVENODD code. EVENODD codes are maximum distance separable (MDS) array codes that are used to protect against erasures, and only require XOR operations for encoding and decoding. We show that when there are two redundancy nodes, to rebuild one erased systematic node, only 3/4 of the information needs to be transmitted. Interestingly, in many cases, the required disk I/O is also minimized. I.

Abstract—Distributed storage systems provide large-scale reliable data storage by storing a certain degree of redundancy in a decentralized fashion on a group of storage nodes. To recover from data losses due to the instability of these nodes, whenever a node leaves the system, additional redundancy should be regenerated to compensate such losses. In this context, the general objective is to minimize the volume of actual network traffic caused by such regenerations. A class of codes, called regenerating codes, has been proposed to achieve an optimal tradeoff curve between the amount of storage space required for storing redundancy and the network traffic during the regeneration. In this paper, we jointly consider the choices of regenerating codes and network topologies. We propose a new design, referred to as RCTREE, that combines the advantage of regenerating codes with a tree-structured regeneration topology. Our focus is the efficient utilization of network links, in addition to the reduction of the regeneration traffic. With the extensive analysis and quantitative evaluations, we show that RCTREE is able to achieve a both fast and stable regeneration, even with departures of storage nodes during the regeneration.

Indistributedstoragesystems,erasurecodesrepresentan attractivesolutiontoaddredundancytostoreddatawhile limitingthestorageoverhead.Theyareabletoprovidethe samereliabilityasreplicationrequiringmuchlessstorage space.Erasurecodingbreaksthedataintopiecesthatare encodedandthenstoredondifferentnodes.However,when storagenodespermanentlyabandonthesystem,newredundantpiecesmustbecreated.Forerasurecodes,generating anewpiecerequiresthetransmissionof kpiecesoverthe network,resultinginaktimeshigherreconstructiontraffic ascomparedtoreplication. Dimakisproposedanewclassofcodes,calledRegeneratingCodes,whichareabletoprovideboththestorage efficiencyoferasurecodesandthecommunicationefficiency of replication.However,Dimakisgaveonlyatheoretical descriptionofthecodeswithoutdiscussingimplementation issues or computationalcosts. We have doneareal implementationofRandomLinearRegeneratingCodesthat allowsustomeasuretheircomputationalcost,whichcan besignificantif the parametersarenotchosenproperly. However, we also find that there exist parameter values thatresultinasignificantreductionofthecommunication overheadattheexpenseofasmallincreaseinstoragecost andcomputation,whichmakesthesecodesveryattractive fordistributedstoragesystems. 1.

Abstract—Peer-to-peer (P2P) storage systems are strongly affected by churn —temporal and permanent peer failures. Because of this churn, the main requirement of such systems is to guarantee that stored objects can always be retrieved. This requirement is specially needed in two main situations: when users want to access the stored objects or when data maintenance processes have to repair lost information. To meet this requirement, exiting P2P storage systems introduce large amounts of redundancy that maintain data availability close to 100%. Unfortunately, these large amounts of redundancy increase the storage costs, either by reducing the overall net capacity or by increasing the communication required for data maintenance. In order to minimize storage costs, P2P storage systems can reduce data redundancy. However, less redundancy means lower data availability, which leads to increase object retrieval times. Unfortunately, longer retrieval times could compromise data maintenance processes and could penalize user’s retrieval times. It is crucial then for P2P storage systems to predict the effects of a redundancy reduction. In order to provide this information, we present a novel analytical framework to measure object retrieval times under different redundancy and churn circumstances. Our framework can be directly used by backup applications aiming to maintain durability at the lower cost, or by data sharing applications that seek to reduce costs by penalizing user retrieval times. We validate our framework by simulation using real P2P traces (Skype and eMule’s KAD). I.

Abstract—In this paper, we present Novasky, a real-world Video-on-Demand (VoD) system capable of delivering cinematicquality video streams to end users. The foundation of the Novasky design is a peer-to-peer (P2P) storage cloud, storing and refreshing media streams in a decentralized fashion using local storage spaces of end users. We present our design objectives in Novasky, and how these objectives are achieved using a collection of unique mechanisms, with respect to caching strategies, coding mechanisms, and the maintenance of the supplydemand relationship when it comes to media availability in the P2P storage cloud. The production Novasky system has been implemented with over 100,000 lines of code. It has been deployed in the Tsinghua University campus network, operational since September 2009, attracting 10,000 users to date, and providing over 1,000 cinematic-quality video streams with bit rates of 1 – 2 Mbps. Based on real-world traces collected over 6 months, we show that Novasky can achieve rapid startups within 4 – 9 seconds, and extremely short seek latencies within 3 seconds. Our empirical experiences with Novasky may bring valuable insights to future designs of production-quality P2P storage cloud systems. I.

Summary. Novel network architectures such as overlay networks offer significant diversity that can compensate for the lack of strict quality of service in today’s communication infrastructures. In order to take advantage of this diversity for delay-sensitive media streaming applications, the network systems can employ efficient mechanisms based on source, channel and even network coding. In particular, fountain codes offer interesting benefits for streaming with server diversity. When they are used independently at each server, they permit to avoid explicit coordination between the senders that only have to provide the receivers with enough innovative packets. In addition, network coding allows for improved throughput and error robustness in multipath transmission where the network nodes participate to increase the symbol diversity in the system. We review in this chapter the most popular rateless codes that enable the deployment of low-cost decentralized communication protocols in self-organized dynamic networks. We then describe their application in distributed multimedia streaming solutions. We further discuss the most popular network coding algorithms in practical media streaming schemes. Finally, we show that hybrid systems based on both rateless coding and network coding can deliver high quality media streams with low computational complexity, as they permit to benefit from both server and path diversity in overlay architectures. 1

Abstract—We develop a framework called DEDI based on differential equations (DE) and differential inclusions (DI) to describe the rank evolution of random network coding (RNC). The DEDI serves as a powerful numerical and analytical tool to study RNC and we demonstrate this via numerical examples as well as an alternate proof of a well known result on RNC – a multicast at rate R exists if and only if a unicast at rate R exists separately for each destination. Index Terms—Random network coding, rank evolution, differential equation, differential inclusion I.

Network coding has recently emerged as an alternative to traditional routing algorithms in communication systems. In network coding, the network nodes combine the packets they receive before forwarding them to the neighbouring nodes. Intensive research efforts have demonstrated that such a processing in the network nodes can provide advantages in terms of throughput or robustness. These potentials, combined with the advent of ad hoc and wireless delivery architectures have triggered the interest of research community about the application of the network coding principles to media streaming applications. This paper describes the potentials of network coding in emerging delivery architectures such as overlay or peerto-peer networks. It overviews the principles of practical network coding algorithms and outlines the challenges posed by multimedia streaming applications. Finally, it provides a survey of the recent work on the application of network coding to media streaming applications, both in wireless or wired communication scenarios. Promising results have been demonstrated but delay and complexity constraints are still posed as the main challenging issues that prevent the wide-scale deployment of network coding algorithms in multimedia communication systems.

Network coding has recently emerged as an alternative to traditional routing algorithms in communication systems. In network coding, the network nodes can combine the packets they receive before forwarding them to the neighbouring nodes. Intensive research efforts have demonstrated that such a processing in the network nodes can provide advantages in terms of throughput or robustness. These potentials, combined with the advent of ad hoc and wireless delivery architectures have triggered the interest of research community about the application of the network coding principles to streaming applications. This paper describes the potentials of network coding in emerging delivery architectures such as overlay or peer-to-peer networks. It overviews the principles of practical network coding algorithms and outlines the challenges posed by multimedia streaming applications. Finally, it provides a survey of the recent work on the application of network coding to media streaming applications, both in wireless or wired communication scenarios. Promising results have been demonstrated where network coding is able to bring benefits in media streaming applications. However, delay and complexity constraints are often posed as the main challenging issues that still prevent the wide-scale deployment of network coding algorithms in multimedia communication.

Abstract—Content distribution over networks is often achieved by using mirror sites that hold copies of files or portions thereof to avoid congestion and delay issues arising from excessive demands to a single location. Accordingly, there are distributed storage solutions that divide the file into pieces and place copies of the pieces (replication) or coded versions of the pieces (coding) at multiple source nodes. We consider a network which uses network coding for multicasting the file. There is a set of source nodes that contains either subsets or coded versions of the pieces of the file. The cost of a given storage solution is defined as the sum of the storage cost and the cost of the flows required to support the multicast. Our interest is in finding the storage capacities and flows at minimum combined cost. We formulate the corresponding optimization problems by using the theory of information measures. In particular, we show that when there are two source nodes, there is no loss in considering subset sources. For three source nodes, we derive a tight upper bound on the cost gap between the coded and uncoded cases. We also present algorithms for determining the content of the source nodes. Index Terms—Content distribution, information measures, minimum cost, network coding.