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Highly Robust Error Correction by Convex Programming
Linear codes decoding of (random) linear codes sparse solutions to underdetermined systems `1 minimization linear programming second-order cone programming the Dantzig selector restricted orthonormality Gaussian random matrices and random projections
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2015/6/17
This paper discusses a stylized communications problem where one wishes to transmit a real-valued signal x ∈ Rn (a block of n pieces of information) to a remote receiver. We ask whether it is possible...
Error Correction via Linear Programming
Linear codes decoding of (random) linear codes sparse solutions to underdetermined systems `1-minimization linear programming restricted orthonormality Gaussian random matrices.
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2015/6/17
Suppose we wish to transmit a vector f ∈ Rn reliably. A frequently discussed approach consists in encoding f with an m by n coding matrix A. Assume now that a fraction of the entries of Af are corrupt...
Dense Error Correction for Low-Rank Matrices via Principal Component Pursuit
Dense Error Correction Low-Rank Matrices Principal Component Pursuit
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2015/6/17
We consider the problem of recovering a lowrank matrix when some of its entries, whose locations are not known a priori, are corrupted by errors of arbitrarily large magnitude. It has recently been sh...
Network error correction with unequal link capacities
Network error correction unequal link capacities
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2010/11/22
This paper studies the capacity of single-source single-sink noiseless networks under adversarial or arbitrary errors on no more than z edges. Unlike prior papers, which assume equal capacities on al...
Construction of Network Error Correction Codes in Packet Networks
Network Error Correction Codes Packet Networks
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2010/11/11
Recently, network error correction coding (NEC) has been studied extensively. Several bounds in classical coding theory have been extended to network error correction coding, especially the Singleton...
The E8 Lattice and Error Correction in Multi-Level Flash Memory
E8 Lattice Error Correction Multi-Level Flash Memory
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2010/12/14
A construction using the E8 lattice and Reed-Solomon codes for error-correction in flash memory is given. Since E8 lattice decoding errors are bursty, a Reed-Solomon code over GF(28) is well suited. T...