Publications [#303197] of Robert Calderbank

Journal articles or Book chapters PUBLISHED

1. Goparaju, S; Tamo, I; Calderbank, R, An improved sub-packetization bound for minimum storage regenerating codes, IEEE Transactions on Information Theory, vol. 60 no. 5 (January, 2014), pp. 2770-2779, Institute of Electrical and Electronics Engineers (IEEE) [1305.3498v1], [doi]
   (last updated on 2026/01/17)

   Abstract:
   Distributed storage systems employ codes to provide resilience to failure of multiple storage disks. In particular, an (n, κ) maximum distance separable (MDS) code stores k symbols in n disks such that the overall system is tolerant to a failure of up to n ? k disks. However, access to at least k disks is still required to repair a single erasure. To reduce repair bandwidth, array codes are used where the stored symbols or packets are vectors of length The MDS array codes have the potential to repair a single erasure using a fraction 1/(n ?κ) of data stored in the remaining disks. We introduce new methods of analysis, which capitalize on the translation of the storage system problem into a geometric problem on a set of operators and subspaces. In particular, we ask the following question: for a given (n, κ), what is the minimum vector-length or subpacketization factor - required to achieve this optimal fraction? For exact recovery of systematic disks in an MDS code of low redundancy, i.e., κ/n > 1/2, the best known explicit codes have a subpacketization factor , which is exponential in k. It has been conjectured that for a fixed number of parity nodes, it is in fact necessary for to be exponential in k. In this paper, we provide a new log-squared converse bound on k for a given -, and prove that k ≤ 2 log2 (logδ +1), for an arbitrary number of parity nodes r = n ? k, where δ = r/(r ? 1). © 1963-2012 IEEE.