Repairable Fountain Codes
Megasthenis Asteris, Alexandros G. Dimakis

TL;DR
This paper introduces a new family of systematic Fountain codes with sparse parities, enabling efficient data recovery and local repair in distributed storage systems through probabilistic analysis of sparse random matrices.
Contribution
The paper presents a novel construction of Fountain codes with sparse parities and logarithmic locality, along with a mathematical analysis of their rank properties.
Findings
Codes can recover original data from slightly more than k encoded symbols.
Single symbol repair requires accessing only O(log k) other symbols.
High probability of perfect matchings in associated sparse bipartite graphs.
Abstract
We introduce a new family of Fountain codes that are systematic and also have sparse parities. Given an input of symbols, our codes produce an unbounded number of output symbols, generating each parity independently by linearly combining a logarithmic number of randomly selected input symbols. The construction guarantees that for any accessing a random subset of encoded symbols, asymptotically suffices to recover the input symbols with high probability. Our codes have the additional benefit of logarithmic locality: a single lost symbol can be repaired by accessing a subset of of the remaining encoded symbols. This is a desired property for distributed storage systems where symbols are spread over a network of storage nodes. Beyond recovery upon loss, local reconstruction provides an efficient alternative for reading symbols that cannot…
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Taxonomy
TopicsAdvanced Data Storage Technologies · Cooperative Communication and Network Coding · Error Correcting Code Techniques
