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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)
An analogy is examined between serially concatenated 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)
Fuzzy commitment schemes, introduced as a link between biometrics and cryptography, are a way to handle biometric data matching as an error-correction issue. We focus here on finding the best error-correcting code with respect to a given database of biometric data. We propose a method that models discrepancies between biometric measurements as an erasure(More)
We design powerful low-density parity-check (LDPC) codes with iterative decoding for the block-fading channel. We first study the case of maximum-likelihood decoding, and show that the design criterion is rather straightforward. Since optimal constructions for maximum-likelihood decoding do not perform well under iterative decoding, we introduce a new(More)
The minimum distance of some families of expander codes is studied, as well as some related families of codes defined on bipartite graphs. The weight spectrum and the minimum distance of a random ensemble of such codes are computed and it is shown that it sometimes meets the Gilbert-Varshamov (GV) bound. A lower bound on the minimum distances of(More)
We describe a new family of integer lattices built from construction A and non-binary LDPC codes. An iterative message-passing algorithm suitable for decoding in high dimensions is proposed. This family of lattices, referred to as LDA lattices, follows the recent transition of Euclidean codes from their classical theory to their modern approach as announced(More)
ÐFault diagnosis of multiprocessor systems motivates the following graph-theoretic definition. A subset g of points in an undirected graph q ˆ …† 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)
Let C be a code of length n over an alphabet of q letters. An n-word y is called a descendant of a set of t codewords x A code is said to have the t-identifying parent property if for any n-word that is a descendant of at most t parents it is possible to identify at least one of them. We prove that for any t ≤ q − 1 there exist sequences of such codes with(More)