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

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