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...tems [18], and redundant disk arrays [3]. Also, LDPC codes and more recently fountain codes [19] were proposed as alternatives with randomized construction and faster encoding and decoding times. See =-=[22]-=- for a practical investigation on using these codes for distributed storage. The key feature of our problem that makes these codes unsuitable is the fact that the data is distributed. We could convert...

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...two ways – either by the number of (redundant) coding nodes required to achieve a baseline of faulttolerance [16, 15], or by the average number of failures tolerated by a given number of coding nodes =-=[21, 30, 27]-=-. Regardless of the evaluation methodology, space optimality may be achieved when the number of coding nodes is equal to the number of failures that may be tolerated. These codes are called Maximum Di...

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...original data [27]. Two most popular examples of erasure coding algorithms are ReedSolomon coding and Low-Density Parity-Check (LDPC) based coding (e.g., Gallager codes, Tornado codes, and IRA codes) =-=[20, 21]-=-. These algorithms differ in the encoding/decoding efficiency, replication factor, and the minimum number of code blocks to reconstruct a message. The selection of the proper erasure coding algorithm ...

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...iciency and fault tolerance. In practice, the exact degree of fault tolerance such codes provide in storage systems is not yet well understood, although there is much recent activity towards this end =-=[14, 13, 6, 4, 5, 7]-=-. To completely understand the fault tolerance of an XORbased erasure code, we must enumerate every set of erasures that leads to data loss. This is necessary because of the irregular structure of suc...

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...c constructions are known (e.g., [19], [20], [21], [22], [23]). The performance, fault tolerance, and reliability of small LDPC codes is also not well understood, though there is much progress (e.g., =-=[24]-=-, [25], [26], [27], [28], [29], [11]). In this paper we provide many constructions of flat XOR-codes, whichinsomesensearesmallLDPC codes, and an analysis to put the storage properties of such construc...

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...ata systems respectively. The availability analysis presented in [8] is intended only to gain insights into the factors affecting availability rather than to derive accurate predictions. Plank et al. =-=[10]-=- describe LDPC erasure codes in the context of peer-to-peer and widely distributed storage systems, and Goodson et al. [5] describe erasurecoded storage that tolerates Byzantine failures. Both these p...

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... optimal value of one. For small values of n and m (less than 1000), there is little theory, and recent work has shown that the techniques developed for asymptotics do not fare well for small n and m =-=[PT04]-=-. The purpose of this paper is to start closing this hole in the theory. Rather than concentrate on large values of n and m, we concentrate on very small values, using enumeration and heuristics to de...

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...egments and builds C coded segments, C ≥ N. If any N out of C coded segments are collected, the original data segments can be decoded [8][18]. A practical investigation of these codes can be found in =-=[22]-=-. As mentioned before, these centralized operations are not suitable for our application environment that involves a large quantity of tiny sensors. An alternative is linear network coding [1][28], wh...

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... timeouts as a complementary failover mechanism in the future. Finally, erasure codes have arisen as a viable alternative to replication for both caching and fault-tolerance in wide-area file systems =-=[5, 14, 19, 21]-=-. In future work, we intend to see how these downloading algorithms apply to file systems based on erasure codes, what additional considerations apply, and what the performance impact is. 7 Acknowledg...