Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rack-Aware Regenerating Codes with Multiple Erasure Tolerance   In a modern distributed storage system, storage nodes are organized in racks,
and the cross-rack communication dominates the system bandwidth. In this paper,
we focus on the rack-aware storage system. The initial setting was immediately
repairing every single node failure. However, multiple node failures are
frequent, and some systems may even wait for multiple nodes failures to occur
before repairing them in order to keep costs down. For the purpose of still
being able to repair them properly when multiple failures occur, we relax the
repair model of the rack-aware storage system. In the repair process, the
cross-rack connections (i.e., the number of helper racks connected for repair
which is called repair degree) and the intra-rack connections (i.e., the number
of helper nodes in the rack contains the failed node) are all reduced. We focus
on minimizing the cross-rack bandwidth in the rack-aware storage system with
multiple erasure tolerances. First, the fundamental tradeoff between the repair
bandwidth and the storage size for functional repair is established. Then, the
two extreme points corresponding to the minimum storage and minimum cross-rack
repair bandwidth are obtained. Second, the explicitly construct corresponding
to the two points are given. Both of them have minimum sub-packetization level
(i.e., the number of symbols stored in each node) and small repair degree.
Besides, the size of underlying finite field is approximately the block length
of the code. Finally, for the convenience of practical use, we also establish a
transformation to convert our codes into systematic codes.

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The categories of this paper are: hep-ex
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-ex