On Expander Codes
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Low-Density Parity-Check Codes: Constructions and Bounds
Low-density parity-check (LDPC) codes were introduced in 1962, but were almost forgotten. The introduction of turbo-codes in 1993 was a real breakthrough in communication theory and practice, due to their practical effectiveness. Subsequently, the connections between LDPC and turbo codes were considered, and it was shown that the latter can be described in the framework of LDPC codes. In recent...
متن کاملEigenvalue bounds on the pseudocodeword weight of expander codes
Four different ways of obtaining low-density parity-check codes from expander graphs are considered. For each case, lower bounds on the minimum stopping set size and the minimum pseudocodeword weight of expander (LDPC) codes are derived. These bounds are compared with the known eigenvalue-based lower bounds on the minimum distance of expander codes. Furthermore, Tanner’s parity-oriented eigenva...
متن کاملLocal Correctability of Expander Codes
In this work, we present the first local-decoding algorithm for expander codes. This yields a new family of constant-rate codes that can recover from a constant fraction of errors in the codeword symbols, and where any symbol of the codeword can be recovered with high probability by reading N symbols from the corrupted codeword, where N is the block-length of the code. Expander codes, introduce...
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Expander codes count among the numerous applications of expander graphs. The term was first coined by Sipser and Spielman when they showed how expander graphs can be used to devise error-correcting codes with large blocklengths that can correct efficiently a constant fraction of errors. This approach has since proved to be a fertile avenue of research that provides insight both into modern iter...
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Quite recently, codes based on real field are gaining momentum in terms of research and applications. In high-performance computing, these codes are being explored to provide fault tolerance under node failures. In this paper, we propose novel real cycle codes based on expander graphs. The requisite graphs are the Ramanujan graphs constructed using incidence matrices of the appropriate projecti...
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We show that expander codes, when properly instantiated, are high-rate list-recoverable codes with linear-time list recovery algorithms. List recoverable codes have been useful recently in constructing efficiently listdecodable codes, as well as explicit constructions of matrices for compressive sensing and group testing. Previous list-recoverable codes with linear-time decoding algorithms have...
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