Explicit MBR All-Symbol Locality Codes

Node failures are inevitable in distributed storage systems (DSS). To enable efficient repair when faced with such failures, two main techniques are known: Regenerating codes, i.e., codes that minimize the total repair bandwidth; and codes with locality, which minimize the number of nodes participating in the repair process. This paper focuses on regenerating codes with locality, using pre-coding based on Gabidulin codes, and presents constructions that utilize minimum bandwidth regenerating (MBR) local codes. The constructions achieve maximum resilience (i.e., optimal minimum distance) and have maximum capacity (i.e., maximum rate). Finally, the same pre-coding mechanism can be combined with a subclass of fractional-repetition codes to enable maximum resilience and repair-by-transfer simultaneously

Storage codes -- coding rate and repair locality

The {\em repair locality} of a distributed storage code is the maximum number of nodes that ever needs to be contacted during the repair of a failed node. Having small repair locality is desirable, since it is proportional to the number of disk accesses during repair. However, recent publications show that small repair locality comes with a penalty in terms of code distance or storage overhead if exact repair is required. Here, we first review some of the main results on storage codes under various repair regimes and discuss the recent work on possible (information-theoretical) trade-offs between repair locality and other code parameters like storage overhead and code distance, under the exact repair regime. Then we present some new information theoretical lower bounds on the storage overhead as a function of the repair locality, valid for all common coding and repair models. In particular, we show that if each of the $n$ nodes in a distributed storage system has storage capacity \ga and if, at any time, a failed node can be {\em functionally} repaired by contacting {\em some} set of $r$ nodes (which may depend on the actual state of the system) and downloading an amount \gb of data from each, then in the extreme cases where \ga=\gb or \ga = r\gb, the maximal coding rate is at most $r/(r+1)$ or 1/2, respectively (that is, the excess storage overhead is at least $1/r$ or 1, respectively).Comment: Accepted for publication in ICNC'13, San Diego, US

An Improved Outer Bound on the Storage-Repair-Bandwidth Tradeoff of Exact-Repair Regenerating Codes

In this paper we establish an improved outer bound on the storage-repair-bandwidth tradeoff of regenerating codes under exact repair. The result shows that in particular, it is not possible to construct exact-repair regenerating codes that asymptotically achieve the tradeoff that holds for functional repair. While this had been shown earlier by Tian for the special case of $[n,k,d]=[4,3,3]$ the present result holds for general $[n,k,d]$. The new outer bound is obtained by building on the framework established earlier by Shah et al.Comment: 14 page

Secure Partial Repair in Wireless Caching Networks with Broadcast Channels

We study security in partial repair in wireless caching networks where parts of the stored packets in the caching nodes are susceptible to be erased. Let us denote a caching node that has lost parts of its stored packets as a sick caching node and a caching node that has not lost any packet as a healthy caching node. In partial repair, a set of caching nodes (among sick and healthy caching nodes) broadcast information to other sick caching nodes to recover the erased packets. The broadcast information from a caching node is assumed to be received without any error by all other caching nodes. All the sick caching nodes then are able to recover their erased packets, while using the broadcast information and the nonerased packets in their storage as side information. In this setting, if an eavesdropper overhears the broadcast channels, it might obtain some information about the stored file. We thus study secure partial repair in the senses of information-theoretically strong and weak security. In both senses, we investigate the secrecy caching capacity, namely, the maximum amount of information which can be stored in the caching network such that there is no leakage of information during a partial repair process. We then deduce the strong and weak secrecy caching capacities, and also derive the sufficient finite field sizes for achieving the capacities. Finally, we propose optimal secure codes for exact partial repair, in which the recovered packets are exactly the same as erased packets.Comment: To Appear in IEEE Conference on Communication and Network Security (CNS