We study a generalization of the setting of regenerating codes, motivated by applications to storage systems consisting of clusters of storage nodes. There are n clusters in total, with m nodes per cluster. A data fil...
详细信息
We study a generalization of the setting of regenerating codes, motivated by applications to storage systems consisting of clusters of storage nodes. There are n clusters in total, with m nodes per cluster. A data file is coded and stored across the mn nodes, with each node storing alpha symbols. For availability of data, we require that the file be retrievable by downloading the entire content from any subset of k clusters. Nodes represent entities that can fail. We distinguish between intra-cluster and inter-cluster bandwidth (BW) costs during node repair. Node-repair in a cluster is accomplished by downloading beta symbols each from any set of d other clusters, dubbed remote helper clusters, and also up to alpha symbols each from any set of l surviving nodes, dubbed local helper nodes, in the host cluster. We first identify the optimal trade-off between storage-overhead and inter-cluster repair-bandwidth under functional repair, and also present optimal exact-repair code constructions for a class of parameters. The new trade-off is strictly better than what is achievable via space-sharing existing coding solutions, whenever l > 0. We then obtain sharp lower bounds on the necessary intra-cluster repair BW to achieve optimal trade-off. Under functional repair, random linear network codes (RLNCs) simultaneously optimize usage of both inter- and intra-cluster repair BW;simulation results based on RLNCs suggest optimality of the bounds on intra-cluster repair-bandwidth. Our bounds reveal the interesting fact that, while it is beneficial to increase the number of local helper nodes f in order to improve the storage-vs-intercluster-repair-BW trade-off, increasing l not only increases intracluster BW in the host-cluster, but also increases the intra-cluster BW in the remote helper clusters. We also analyze resilience of the clustered storage system against passive eavesdropping by providing file-size bounds and optimal code constructions.
This paper studies new bounds and code constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain...
详细信息
This paper studies new bounds and code constructions that are applicable to the combinatorial granular channel model previously introduced by Sharov and Roth. We derive new bounds on the maximum cardinality of a grain-error-correcting code and propose constructions of codes that correct grain-errors. We demonstrate that a permutation of the classical group codes (e.g., Constantin-Rao codes) can correct a single grain-error. In many cases of interest, our results improve upon the currently best known bounds and constructions. Some of the approaches adopted in the context of grain-errors may have application to related channel models.
Memristors, also known as resistive RAMs, are very promising non-volatile media that can be packed in unprecedented density. However, the crossbar layout by which this high density is achieved entails major challenges...
详细信息
ISBN:
(纸本)9781479946655
Memristors, also known as resistive RAMs, are very promising non-volatile media that can be packed in unprecedented density. However, the crossbar layout by which this high density is achieved entails major challenges arising from cell-to-cell interference. In particular, cell readout is affected by sneak paths, which are electric paths passing through other crossbar cells and affecting the outcome of the read operation. The existence of sneak paths and their severity depends upon the current bit assignment stored in the array. In this paper we study sneak-path errors by modeling the array as a single-parameter information theoretic channel. We calculate this parameter in closed form as a function of the array dimensions and the bias between 0s and 1s in the written bits. We extend this result to the case where error occurs only when at least L sneak-paths exist, and also examine the correlation between sneak-path errors in different cells within the array. The channel capacity is calculated in a flavor similar to the capacity of the Z channel, only with transition probability that depends on the array-bit distribution.
Rank modulation schemes for non-volatile memories (NVMs) represent information by the relative rankings of cell charge levels. This approach has several benefits;in particular, the scheme resolves the "write-asym...
详细信息
ISBN:
(纸本)9781479913213
Rank modulation schemes for non-volatile memories (NVMs) represent information by the relative rankings of cell charge levels. This approach has several benefits;in particular, the scheme resolves the "write-asymmetry" limitation that NVMs suffer from. However, cell writing is still affected by a common NVM problem: inter-cell coupling, which can result in inadvertently increasing the charge level of neighboring cells. This is a potential source of error in the rank modulation scheme. In this paper, we explore the idea of constrained coding over permutations. These constraints minimize the impact of inter-cell coupling while still allowing the use of the rank modulation scheme. We study various constraints and their resulting rates, capacities, and other properties, and introduce an explicit constrained rank modulation code construction.
暂无评论