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Reliability is essential for storing files in many applications ofdistributed storage systems. To maintain reliability, when a storage nodefails, a new node should be regenerated by a repair process. Most of theprevious results on the repair problem assume perfect (error-free) links in thenetworks. However, in practice, especially in a wireless network, thetransmitted packets (for repair) may be lost due to, e.g., link failure orbuffer overflow. We study the repair problem of distributed storage systems inpacket erasure networks, where a packet loss is modeled as an erasure. Theminimum repair-bandwidth, namely the amount of information sent from thesurviving nodes to the new node, is established under the ideal assumption ofinfinite number of packet transmissions. We also study the bandwidth-storagetradeoffs in erasure networks. Then, the use of repairing storage nodes (nodeswith smaller storage space) is proposed to reduce the repair-bandwidth. Westudy the minimal storage of repairing storage nodes. For the case of a finitenumber of packet transmissions, the probability of successful repairing isinvestigated. We show that the repair with a finite number of packettransmissions may use much larger bandwidth than the minimum repair-bandwidth.Finally, we propose a combinatorial optimization problem, which results in theoptimal repair-bandwidth for the given packet erasure probability and finitepacket transmissions.

Repair for Distributed Storage Systems in Packet Erasure Networks