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https://feeds.library.caltech.edu/people/Wang-Zhiying/combined.rss
A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 16:12:19 +0000On the capacity of bounded rank modulation for flash memories
https://resolver.caltech.edu/CaltechPARADISE:2008.ETR091
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Jiang-Anxiao-Andrew', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2009
Rank modulation has been recently introduced as a new information representation scheme for flash memories.
Given the charge levels of a group of flash cells, sorting
is used to induce a permutation, which in turn represents
data. Motivated by the lower sorting complexity of smaller
cell groups, we consider bounded rank modulation, where
a sequence of permutations of given sizes are used to
represent data. We study the capacity of bounded rank
modulation under the condition that permutations can
overlap for higher capacity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/pe2zr-nrj54On the capacity of bounded rank modulation for flash memories
https://resolver.caltech.edu/CaltechAUTHORS:20100816-142932373
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Jiang-Anxiao-Andrew', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2009
DOI: 10.1109/ISIT.2009.5205972
Rank modulation has been introduced as a new information representation scheme for flash memories. Given the charge levels of a group of flash cells, sorting is used to induce a permutation, which in turn represents data. Motivated by the lower sorting complexity of smaller cell groups, we consider bounded rank modulation, where a sequence of permutations of given sizes are used to represent data. We study the capacity of bounded rank modulation under the condition that permutations can overlap for higher capacity.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7f210-bjx91Partial Rank Modulation for Flash Memories
https://resolver.caltech.edu/CaltechAUTHORS:20110331-130545474
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2010
DOI: 10.1109/ISIT.2010.5513597
Rank modulation was recently proposed as an information representation for multilevel flash memories, using permutations or ranks of n flash cells. The current decoding process finds the cell with the i-th highest charge level at iteration i, for i = 1, 2,...,n - 1. Motivated by the need to reduce the number of such iterations, we consider k-partial permutations, where only the highest k cell levels are considered for information representation. We propose a generalization of Gray codes for k-partial permutations such that information is updated efficiently.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dzswn-2ar83Rebuilding for Array Codes in Distributed Storage Systems
https://resolver.caltech.edu/CaltechPARADISE:2010.ETR103
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Dimakis-A-G', 'name': {'family': 'Dimakis', 'given': 'Alexandros G.'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2010
In distributed storage systems that use coding, the issue of minimizing the communication required to rebuild a storage node after a failure arises. We consider the problem of repairing an erased node in a distributed storage system that uses an EVENODD code. EVENODD codes are maximum distance separable (MDS) array codes that are used to protect against erasures, and only require XOR operations for encoding and decoding. We show that when there are two redundancy nodes, to rebuild one erased systematic node, only 3=4 of the information needs to be transmitted. Interestingly, in many cases, the required disk I/O is also minimized.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/h4jxr-xyf21Rebuilding for Array Codes in Distributed Storage Systems
https://resolver.caltech.edu/CaltechAUTHORS:20110707-082718436
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Dimakis-A-G', 'name': {'family': 'Dimakis', 'given': 'Alexandros G.'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2010
DOI: 10.1109/GLOCOMW.2010.5700274
In distributed storage systems that use coding, the issue of minimizing the communication required to rebuild a storage node after a failure arises. We consider the problem of repairing an erased node in a distributed storage system that uses an EVENODD code. EVENODD codes are maximum distance separable (MDS) array codes that are used to protect against erasures, and only require XOR operations for encoding and decoding. We show that when there are two redundancy nodes, to rebuild one erased systematic node, only 3/4 of the information needs to be transmitted. Interestingly, in many cases, the required disk I/O is also minimized.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/fd7qm-72d07MDS Array Codes with Optimal Rebuilding
https://resolver.caltech.edu/CaltechPARADISE:2011.ETR110
Authors: {'items': [{'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2011
DOI: 10.48550/arXiv.1103.3737
MDS array codes are widely used in storage systems
to protect data against erasures. We address the rebuilding ratio
problem, namely, in the case of erasures, what is the the fraction
of the remaining information that needs to be accessed in order
to rebuild exactly the lost information? It is clear that when the
number of erasures equals the maximum number of erasures
that an MDS code can correct then the rebuilding ratio is 1
(access all the remaining information). However, the interesting
(and more practical) case is when the number of erasures is
smaller than the erasure correcting capability of the code. For
example, consider an MDS code that can correct two erasures:
What is the smallest amount of information that one needs to
access in order to correct a single erasure? Previous work showed
that the rebuilding ratio is bounded between 1/2 and 3/4 , however,
the exact value was left as an open problem. In this paper, we
solve this open problem and prove that for the case of a single
erasure with a 2-erasure correcting code, the rebuilding ratio is
1/2 . In general, we construct a new family of r-erasure correcting
MDS array codes that has optimal rebuilding ratio of 1/r
in the
case of a single erasure. Our array codes have efficient encoding
and decoding algorithms (for the case r = 2 they use a finite field
of size 3) and an optimal update property.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vp0h3-kfs88Patterned cells for phase change memories
https://resolver.caltech.edu/CaltechAUTHORS:20170213-160905267
Authors: {'items': [{'id': 'Jiang-Anxiao-Andrew', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2011
DOI: 10.1109/ISIT.2011.6033979
Phase-change memory (PCM) is an emerging nonvolatile memory technology that promises very high performance. It currently uses discrete cell levels to represent data, controlled by a single amorphous/crystalline domain in a cell. To improve data density, more levels per cell are needed. There exist a number of challenges, including cell programming noise, drifting of cell levels, and the high power requirement for cell programming. In this paper, we present a new cell structure called patterned cell, and explore its data representation schemes. Multiple domains per cell are used, and their connectivity is used to store data. We analyze its storage capacity, and study its error-correction capability and the construction of error-control codes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/dpzzx-7bf24MDS Array Codes with Optimal Rebuilding
https://resolver.caltech.edu/CaltechAUTHORS:20120406-093959188
Authors: {'items': [{'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2011
DOI: 10.1109/ISIT.2011.6033733
MDS array codes are widely used in storage systems to protect data against erasures. We address the rebuilding ratio problem, namely, in the case of erasures, what is the the fraction of the remaining information that needs to be accessed in order to rebuild exactly the lost information? It is clear that when the number of erasures equals the maximum number of erasures that an MDS code can correct then the rebuilding ratio is 1 (access all the remaining information). However, the interesting (and more practical) case is when the number of erasures is smaller than the erasure correcting capability of the code. For example, consider an MDS code that can correct two erasures: What is the smallest amount of information that one needs to access in order to correct a single erasure? Previous work showed that the rebuilding ratio is bounded between 1/2 and 3/4, however, the exact value was left as an open problem. In this paper, we solve this open problem and prove that for the case of a single erasure with a 2-erasure correcting code, the rebuilding ratio is 1/2. In general, we construct a new family of r-erasure correcting MDS array codes that has optimal rebuilding ratio of 1/r in the case of a single erasure. Our array codes have efficient encoding and decoding algorithms (for the case r = 2 they use a finite field of size 3) and an optimal update property.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/2rrs6-0d438On Codes for Optimal Rebuilding Access
https://resolver.caltech.edu/CaltechPARADISE:2011.ETR111
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2011
DOI: 10.48550/arXiv.1107.1627
MDS (maximum distance separable) array codes
are widely used in storage systems due to their computationally
efficient encoding and decoding procedures. An MDS code with
r redundancy nodes can correct any r erasures by accessing
(reading) all the remaining information in both the systematic
nodes and the parity (redundancy) nodes. However, in practice,
a single erasure is the most likely failure event; hence, a natural
question is how much information do we need to access in order
to rebuild a single storage node? We define the rebuilding ratio
as the fraction of remaining information accessed during the
rebuilding of a single erasure. In our previous work we showed
that the optimal rebuilding ratio of 1/r is achievable (using
our newly constructed array codes) for the rebuilding of any
systematic node, however, all the information needs to be accessed
for the rebuilding of the parity nodes. Namely, constructing array
codes with a rebuilding ratio of 1/r was left as an open problem.
In this paper, we solve this open problem and present array codes
that achieve the lower bound of 1/r for rebuilding any single
systematic or parity node.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/vz336-bdm65Patterned Cells for Phase Change Memories
https://resolver.caltech.edu/CaltechAUTHORS:20120502-130441311
Authors: {'items': [{'id': 'Jiang-Anxiao-Andrew', 'name': {'family': 'Jiang', 'given': 'Anxiao (Andrew)'}}, {'id': 'Zhou-Hongchao', 'name': {'family': 'Zhou', 'given': 'Hongchao'}}, {'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2012
Phase-change memory (PCM) is an emerging nonvolatile memory technology that promises very high performance.
It currently uses discrete cell levels to represent data, controlled
by a single amorphous/crystalline domain in a cell. To improve
data density, more levels per cell are needed. There exist a number of challenges, including cell programming noise, drifting of
cell levels, and the high power requirement for cell programming.
In this paper, we present a new cell structure called patterned cell, and explore its data representation schemes. Multiple
domains per cell are used, and their connectivity is used to
store data. We analyze its storage capacity, and study its error-correction capability and the construction of error-control codes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/6n5zz-gsa64Long MDS Codes for Optimal Repair Bandwidth
https://resolver.caltech.edu/CaltechAUTHORS:20120616-221646611
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2012
MDS codes are erasure-correcting codes that can
correct the maximum number of erasures given the number of
redundancy or parity symbols. If an MDS code has r parities
and no more than r erasures occur, then by transmitting all
the remaining data in the code one can recover the original
information. However, it was shown that in order to recover a
single symbol erasure, only a fraction of 1/r of the information
needs to be transmitted. This fraction is called the repair
bandwidth (fraction). Explicit code constructions were given in
previous works. If we view each symbol in the code as a vector
or a column, then the code forms a 2D array and such codes
are especially widely used in storage systems. In this paper, we
ask the following question: given the length of the column l, can
we construct high-rate MDS array codes with optimal repair
bandwidth of 1/r, whose code length is as long as possible? In
this paper, we give code constructions such that the code length
is (r + 1)log_r l.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xt2bt-jdt16Long MDS Codes for Optimal Repair Bandwidth
https://resolver.caltech.edu/CaltechAUTHORS:20130204-132322886
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2012
DOI: 10.1109/ISIT.2012.6283041
MDS codes are erasure-correcting codes that can correct the maximum number of erasures given the number of redundancy or parity symbols. If an MDS code has r parities and no more than r erasures occur, then by transmitting all the remaining data in the code one can recover the original information. However, it was shown that in order to recover a single symbol erasure, only a fraction of 1/r of the information needs to be transmitted. This fraction is called the repair bandwidth (fraction). Explicit code constructions were given in previous works. If we view each symbol in the code as a vector or a column, then the code forms a 2D array and such codes are especially widely used in storage systems. In this paper, we ask the following question: given the length of the column l, can we construct high-rate MDS array codes with optimal repair bandwidth of 1/r, whose code length is as long as possible? In this paper, we give code constructions such that the code length is (r + l)log_r l.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/gktdd-nq646Long MDS Codes for Optimal Repair Bandwidth
https://resolver.caltech.edu/CaltechAUTHORS:20120829-103740126
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2012
DOI: 10.1109/ISIT.2012.6283041
MDS codes are erasure-correcting codes that can correct the maximum number of erasures given the number of redundancy or parity symbols. If an MDS code has r parities and no more than r erasures occur, then by transmitting all the remaining data in the code one can recover the original information. However, it was shown that in order to recover a single symbol erasure, only a fraction of 1/r of the information needs to be transmitted. This fraction is called the repair bandwidth (fraction). Explicit code constructions were given in previous works. If we view each symbol in the code as a vector or a column, then the code forms a 2D array and such codes are especially widely used in storage systems. In this paper, we ask the following question: given the length of the column l, can we construct high-rate MDS array codes with optimal repair bandwidth of 1/r, whose code length is as long as possible? In this paper, we give code constructions such that the code length is (r + l)logr l.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/hgwxz-m6n08Access vs. Bandwidth in Codes for Storage
https://resolver.caltech.edu/CaltechAUTHORS:20120829-092120549
Authors: {'items': [{'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2012
DOI: 10.1109/ISIT.2012.6283042
Maximum distance separable (MDS) codes are widely used in storage systems to protect against disks (nodes) failures. An (n, k, l) MDS code uses n nodes of capacity l to store k information nodes. The MDS property guarantees the resiliency to any n − k node failures. An optimal bandwidth (resp. optimal access) MDS code communicates (resp. accesses) the minimum amount of data during the recovery process of a single failed node. It was shown that this amount equals a fraction of 1/(n − k) of data stored in each node. In previous optimal bandwidth constructions, l scaled polynomially with k in codes with asymptotic rate < 1. Moreover, in constructions with constant number of parities, i.e. rate approaches 1, l scaled exponentially w.r.t. k. In this paper we focus on the practical case of n − k = 2, and ask the following question: Given the capacity of a node l what is the largest (w.r.t. k) optimal bandwidth (resp. access) (k + 2, k, l) MDS code. We give an upper bound for the general case, and two tight bounds in the special cases of two important families of codes.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/8ne9e-4q567Codes for Network Switches
https://resolver.caltech.edu/CaltechAUTHORS:20130128-153803180
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Shaked-O', 'name': {'family': 'Shaked', 'given': 'Omer'}}, {'id': 'Cassuto-Y', 'name': {'family': 'Cassuto', 'given': 'Yuval'}, 'orcid': '0000-0001-6369-6699'}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2013
A network switch routes data packets between its
multiple input and output ports. Packets from input ports are
stored upon arrival in a switch fabric comprising multiple
memory banks. This can result in memory contention when
distinct output ports request packets from the same memory
bank, resulting in a degraded switching bandwidth. To solve this
problem, we propose to add redundant memory banks for storing
the incoming packets. The problem we address is how to minimize
the number of redundant memory banks given some guaranteed
contention resolution capability. We present constructions of
new switch memory architectures based on different coding
techniques. The codes allow decreasing the redundancy by 1/2
or 2/3, depending on the request specifications, compared to
non-coding solutions.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/7ct46-a3j12Zigzag Codes: MDS Array Codes With Optimal Rebuilding
https://resolver.caltech.edu/CaltechAUTHORS:20130321-102330661
Authors: {'items': [{'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2013
DOI: 10.1109/TIT.2012.2227110
Maximum distance separable (MDS) array codes are widely used in storage systems to protect data against erasures. We address the rebuilding ratio problem, namely, in the case of erasures, what is the fraction of the remaining information that needs to be accessed in order to rebuild exactly the lost information? It is clear that when the number of erasures equals the maximum number of erasures that an MDS code can correct, then the rebuilding ratio is 1 (access all the remaining information). However, the interesting and more practical case is when the number of erasures is smaller than the erasure correcting capability of the code. For example, consider an MDS code that can correct two erasures: What is the smallest amount of information that one needs to access in order to correct a single erasure? Previous work showed that the rebuilding ratio is bounded between 1/2 and 3/4; however, the exact value was left as an open problem. In this paper, we solve this open problem and prove that for the case of a single erasure with a two-erasure correcting code, the rebuilding ratio is 1/2. In general, we construct a new family of r-erasure correcting MDS array codes that has optimal rebuilding ratio of 1/(r) in the case of a single erasure. Our array codes have efficient encoding and decoding algorithms (for the cases r=2 and r=3, they use a finite field of size 3 and 4, respectively) and an optimal update property.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/c80wj-h6a11Access Versus Bandwidth in Codes for Storage
https://resolver.caltech.edu/CaltechAUTHORS:20140425-151109319
Authors: {'items': [{'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2014
DOI: 10.1109/TIT.2014.2305698
Maximum distance separable (MDS) codes are widely used in storage systems to protect against disk (node) failures. A node is said to have capacity l over some field F, if it can store that amount of symbols of the field. An (n, k, l) MDS code uses n nodes of capacity l to store k information nodes. The MDS property guarantees the resiliency to any n-k node failures. An optimal bandwidth (respectively, optimal access) MDS code communicates (respectively, accesses) the minimum amount of data during the repair process of a single failed node. It was shown that this amount equals a fraction of 1/(n - k) of data stored in each node. In previous optimal bandwidth constructions, l scaled polynomially with k in codes when the asymptotic rate is less than 1. Moreover, in constructions with a constant number of parities, i.e., when the rate approaches 1, l is scaled exponentially with k. In this paper, we focus on the case of linear codes with linear repair operations and constant number of parities n - k = r, and ask the following question: given the capacity of a node l what is the largest number of information disks k in an optimal bandwidth (respectively, access) (k + r, k, l) MDS code? We give an upper bound for the general case, and two tight bounds in the special cases of two important families of codes. The first is a family of codes with optimal update property, and the second is a family with optimal access property. Moreover, the bounds show that in some cases optimal-bandwidth codes have larger k than optimal-access codes, and therefore these two measures are not equivalent.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/677nb-sgx08Explicit MDS Codes for Optimal Repair Bandwidth
https://resolver.caltech.edu/CaltechAUTHORS:20160120-152728882
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2016
DOI: 10.48550/arXiv.1411.6328
MDS codes are erasure-correcting codes that can correct the maximum number of erasures for a given number of
redundancy or parity symbols. If an MDS code has r parities and no more than r erasures occur, then by transmitting
all the remaining data in the code, the original information can be recovered. However, it was shown that in order
to recover a single symbol erasure, only a fraction of 1/r of the information needs to be transmitted. This fraction
is called the repair bandwidth (fraction). Explicit code constructions were given in previous works. If we view each
symbol in the code as a vector or a column over some field, then the code forms a 2D array and such codes are
especially widely used in storage systems. In this paper, we address the following question: given the length of the
column l, number of parities r, can we construct high-rate MDS array codes with optimal repair bandwidth of 1/r,
whose code length is as long as possible? In this paper, we give code constructions such that the code length is
(r +1) log_r l.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/xmt8m-whw26Explicit Minimum Storage Regenerating Codes
https://resolver.caltech.edu/CaltechAUTHORS:20160930-131654865
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Tamo-Itzhak', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2016
DOI: 10.1109/TIT.2016.2553675
In distributed storage, a file is stored in a set of nodes and protected by erasure-correcting codes. Regenerating code is a type of code with two properties: first, it can reconstruct the entire file in the presence of any r node erasures for some specified integer r; second, it can efficiently repair an erased node from any subset of remaining nodes with a given size. In the repair process, the amount of information transmitted from each node normalized by the storage size per node is termed repair bandwidth (fraction). When the storage size per node is minimized, the repair bandwidth is lower bounded by 1/r, where r is the number of parity nodes. A code attaining this lower bound is said to have optimal repair. We consider codes with minimum storage size per node and optimal repair, called minimum storage regenerating (MSR) codes. In particular, if an MSR code has r parities and any r erasures occur, then by transmitting all the information from the remaining nodes, the original file can be reconstructed. On the other hand, if only one erasure occurs, only a fraction of 1/r of the information in each remaining node needs to be transmitted. If we view each node as a vector or a column over some field, then the code forms a 2-D array. Given the length of the column l and the number of parities r, we explicitly construct the high-rate MSR codes. The number of systematic nodes of our construction is (r + 1) log_rl, which is longer than previously known results. Besides, we construct the MSR codes with other desirable properties: first, the codes with low complexity when the information is updated, and second, the codes with low access or storage node I/O cost during repair.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/17jmt-mh471Optimal Rebuilding of Multiple Erasures in MDS Codes
https://resolver.caltech.edu/CaltechAUTHORS:20170119-080421044
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Tamo-Itzhak', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2017
DOI: 10.1109/TIT.2016.2633411
Maximum distance separable (MDS) array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with r redundancy nodes can correct any r node erasures by accessing (reading) all the remaining information in the surviving nodes. However, in practice, e erasures are a more likely failure event, for some 1≤ehttps://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/bk2bc-4f252Switch Codes: Codes for Fully Parallel Reconstruction
https://resolver.caltech.edu/CaltechAUTHORS:20170315-151626957
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Kiah-Han-Mao', 'name': {'family': 'Kiah', 'given': 'Han Mao'}}, {'id': 'Cassuto-Y', 'name': {'family': 'Cassuto', 'given': 'Yuval'}, 'orcid': '0000-0001-6369-6699'}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2017
DOI: 10.1109/TIT.2017.2664867
Network switches and routers scale in rate by distributing the packet read/write operations across multiple memory banks. Rate scaling is achieved so long as sufficiently many packets can be written and read in parallel. However, due to the non-determinism of the read process, parallel pending read requests may contend on memory banks, and thus significantly lower the switching rate. In this paper, we provide a constructive study of codes that guarantee fully parallel data reconstruction without contention. We call these codes "switch codes," and construct three optimal switch-code families with different parameters. All the constructions use only simple XOR-based encoding and decoding operations, an important advantage when operated in ultra-high speeds. Switch codes achieve their good performance by spanning simultaneous disjoint local-decoding sets for all their information symbols. Switch codes may be regarded as an extreme version of the previously studied batch codes, where the switch version requires parallel reconstruction of all the information symbols.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/323t5-36794On Codes for Optimal Rebuilding Access
https://resolver.caltech.edu/CaltechAUTHORS:20191004-150559432
Authors: {'items': [{'id': 'Wang-Zhiying', 'name': {'family': 'Wang', 'given': 'Zhiying'}}, {'id': 'Tamo-I', 'name': {'family': 'Tamo', 'given': 'Itzhak'}}, {'id': 'Bruck-J', 'name': {'family': 'Bruck', 'given': 'Jehoshua'}, 'orcid': '0000-0001-8474-0812'}]}
Year: 2019
DOI: 10.48550/arXiv.1107.1627
MDS (maximum distance separable) array codes are widely used in storage systems due to their computationally efficient encoding and decoding procedures. An MDS code with r redundancy nodes can correct any r erasures by accessing (reading) all the remaining information in both the systematic nodes and the parity (redundancy) nodes. However, in practice, a single erasure is the most likely failure event; hence, a natural question is how much information do we need to access in order to rebuild a single storage node? We define the rebuilding ratio as the fraction of remaining information accessed during the rebuilding of a single erasure. In our previous work we showed that the optimal rebuilding ratio of 1/r is achievable (using our newly constructed array codes) for the rebuilding of any systematic node, however, all the information needs to be accessed for the rebuilding of the parity nodes. Namely, constructing array codes with a rebuilding ratio of 1/r was left as an open problem. In this paper, we solve this open problem and present array codes that achieve the lower bound of 1/r for rebuilding any single systematic or parity node.https://authors.library.caltech.eduhttps://authors.library.caltech.edu/records/necdh-j6n98