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33,935
On Lattices, Learning with Errors, Random Linear Codes, and Cryptography
 In STOC
, 2005
"... Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear co ..."
Abstract

Cited by 364 (6 self)
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Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certain learning problem. This learning problem is a natural extension of the ‘learning from parity with error’ problem to higher moduli. It can also be viewed as the problem of decoding from a random linear
On the ListDecodability of Random Linear Codes
"... Abstract—The listdecodability of random linear codes is shown to be as good as that of general random codes. Specifically, for every fixed finite field Fq, p ∈ (0, 1 − 1/q) and ε>0, itis proved that with high probability a random linear code C in F n q of rate (1 − Hq(p) − ε) can be list decode ..."
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Cited by 8 (2 self)
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Abstract—The listdecodability of random linear codes is shown to be as good as that of general random codes. Specifically, for every fixed finite field Fq, p ∈ (0, 1 − 1/q) and ε>0, itis proved that with high probability a random linear code C in F n q of rate (1 − Hq(p) − ε) can be list
Differentiated Data Persistence with Priority Random Linear Codes
, 2006
"... Both peertopeer and sensor networks have the fundamental characteristics of node churn and failures. Peers in P2P networks are highly dynamic, whereas sensors are not dependable. As such, maintaining the persistence of periodically measured data in a scalable fashion has become a critical challeng ..."
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Cited by 25 (2 self)
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challenge in such systems, without the use of centralized servers. To better cope with node dynamics and failures, we propose priority random linear codes, as well as their affiliated predistribution protocols, to maintain measurement data in different priorities, such that critical data have a higher
Geometric Random Linear Codes in Sensor Networks
"... Wireless sensor networks consist of unreliable and energyconstrained sensors connecting to each other wirelessly. As measured data may be lost due to sensor failures, maintaining the persistence of periodically measured data in a scalable fashion has become a critical challenge in sensor networks, ..."
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Cited by 5 (0 self)
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, without the use of centralized servers. To cope with node failures, while providing convenient access to measured data, we propose geometric random linear codes, to encode data in a hierarchical fashion in geographic regions with different sizes, such that data are easy to access, if the original sensors
Differentiated Data Persistence with Priority Random Linear Codes
"... Both peertopeer and sensor networks have the fundamental characteristics of node churn and failures. Peers in P2P networks are highly dynamic, whereas sensors are not dependable. As such, maintaining the persistence of periodically measured data in a scalable fashion has become a critical challeng ..."
Abstract
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challenge in such systems, without the use of centralized servers. To better cope with node dynamics and failures, we propose priority random linear codes, as well as their affiliated predistribution protocols, to maintain measurement data in different priorities, such that critical data have a higher
Differentiated Data Persistence with Priority Random Linear Codes
"... Both peertopeer and sensor networks have the fundamental characteristics of node churn and failures. Peers in P2P networks are highly dynamic, whereas sensors are not dependable. As such, maintaining the persistence of periodically measured data in a scalable fashion has become a critical challeng ..."
Abstract
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challenge in such systems, without the use of centralized servers. To better cope with node dynamics and failures, we propose priority random linear codes, as well as their affiliated predistribution protocols, to maintain measurement data in different priorities, such that critical data have a higher
Sparse random linear codes are locally decodable and testable
 in Proc. 40th STOC
, 2007
"... We show that random sparse binary linear codes are locally testable and locally decodable (under any linear encoding) with constant queries (with probability tending to one). By sparse, we mean that the code should have only polynomially many codewords. Our results are the first to show that local d ..."
Abstract

Cited by 17 (6 self)
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We show that random sparse binary linear codes are locally testable and locally decodable (under any linear encoding) with constant queries (with probability tending to one). By sparse, we mean that the code should have only polynomially many codewords. Our results are the first to show that local
On Lattices, Learning with Errors,Random Linear Codes, and Cryptography
, 2004
"... Abstract Our main result is a reduction from worstcase lattice problems such as SVP and SIVP to a certainlearning problem. This learning problem is a natural extension of the `learning from parity with error' problem to higher moduli. It can also be viewed as the problem of decoding from a ran ..."
Abstract
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random linear code.This, we believe, gives a strong indication that these problems are hard. Our reduction, however, is quantum. Hence, an efficient solution to the learning problem implies a quantum algorithm for SVP andSIVP. A main open question is whether this reduction can be made classical. Using
How good is random linear coding based distributed networked storage
 In NetCod
, 2005
"... Abstract — We consider the problem of storing a large file or multiple large files in a distributed manner over a network. In the framework we consider, there are multiple storage locations, each of which only have very limited storage space for each file. Each storage location chooses a part (or a ..."
Abstract

Cited by 99 (15 self)
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based storage, random linear coding based storage motivated by network coding. We demonstrate that, in principle, a traditional erasure coding based storage (eg: ReedSolomon Codes) strategy can almost do as well as one can ask for with appropriate choice of parameters. However, the cost is a large
Improved Delay Estimates for a Queueing Model for Random Linear Coding for Unicast
, 901
"... Abstract—Consider a lossy communication channel for unicast with zerodelay feedback. For this communication scenario, a simple retransmission scheme is optimum with respect to delay. An alternative approach is to use random linear coding in automatic repeatrequest (ARQ) mode. We extend the work of ..."
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Abstract—Consider a lossy communication channel for unicast with zerodelay feedback. For this communication scenario, a simple retransmission scheme is optimum with respect to delay. An alternative approach is to use random linear coding in automatic repeatrequest (ARQ) mode. We extend the work
Results 1  10
of
33,935