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This paper presents a new erasure code called Treeplication designed fordistributed recovery of the full information word, while most prior work incoding for distributed storage only supports distributed repair of individualsymbols. A Treeplication code for $k$ information symbols is defined on abinary tree with $2k-1$ vertices, along with a distribution for selecting codesymbols from the tree layers. We analyze and optimize the code under arandom-multiset model, which captures the system property that the nodesavailable for recovery are drawn randomly from the nodes storing the codesymbols. Treeplication codes are shown to have full-recovery communication-costcomparable to replication, while offering much better recoverability.

Treeplication: An Erasure Code for Distributed Full Recovery under the Random Multiset Channel