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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… (More)

1725 band-limited functions. The decoders are still convolutional, and thus democratic; in his construction, the rate of the exponential decay of the error, shown here to be necessarily strictly inferior to 1, is smaller than 1 by several orders of magnitude. ACKNOWLEDGMENT The authors would like to thank Ron DeVore and C. Sinan Güntürk for helpful… (More)

—An analogy is examined between serially concate-nated codes and parallel concatenations whose interleavers are described by bipartite graphs with good expanding properties. In particular, a modified expander code construction is shown to behave very much like Forney's classical concatenated codes, though with improved decoding complexity. It is proved that… (More)

We study the minimum distance of codes defined on bipartite graphs. Weight spectrum and the minimum distance of a random ensemble of such codes are computed. It is shown that if the vertex codes have minimum distance ≥ 3, the overall code is asymptotically good, and sometimes meets the Gilbert-Varshamov bound. Constructive families of expander codes are… (More)

Fuzzy sketches, introduced as a link between biometry and cryptography, are a way of handling biometric data matching as an error correction issue. We focus here on iris biometrics and look for the best error-correcting code in that respect. We show that two-dimensional iterative min-sum decoding leads to results near the theoretical limits. In particular,… (More)

ÐFault diagnosis of multiprocessor systems motivates the following graph-theoretic definition. A subset g of points in an undirected graph q
Y i is called an identifying code if the sets f
v g consisting of all elements of g within distance one from the vertex v are different. We also require that the sets f
v g are all nonempty. We take q to be… (More)