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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...
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...