Gilles Zémor

On expander codes

Sipser and Spielman (see ibid., vol.42, p.1717-22, Nov. 1996) have introduced a constructive family of asymptotically good linear error-correcting codes-expander codes-together with a simple parallel algorithm that will always remove a constant fraction of errors. We introduce a variation on their decoding algorithm that, with no extra cost in complexity, provably corrects up to 12 times more errors.

Optimal Iris Fuzzy Sketches

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, we experiment our techniques on the iris challenge evaluation (ICE) database and validate our findings.

Error exponents of expander codes

We show that expander codes attain the capacity of the binary-symmetric channel under iterative decoding. The error probability has a positive exponent for all rates between zero and the channel capacity. The decoding complexity grows linearly with the code length.

Low-Density Parity-Check Codes for Nonergodic Block-Fading Channels

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 family of full-diversity LDPC codes that exhibit near-outage-limit performance under iterative decoding for all block-lengths. This family competes favorably with multiplexed parallel turbo codes for nonergodic channels.

Theoretical and Practical Boundaries of Binary Secure Sketches

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 and error channel, and we estimate its capacity. We then show that two-dimensional iterative min-sum decoding of properly chosen product codes almost reaches the capacity of this channel. This leads to practical fuzzy commitment schemes that are close to theoretical limits. We test our techniques on public iris and fingerprint databases and validate our findings.

A Hypergraph Approach to the Identifying Parent Property: The Case of Multiple Parents

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 x1, . . . ,xt if

Multidimensional reconciliation for a continuous-variable quantum key distribution

y_i\in\{x^1_i,\dots,x^t_i\}

Hashing with SL2

for all i=1, . . . ,n. 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

Intersecting codes and independent families

t\le q-1

Error-correcting WOM-codes

there exist sequences of such codes with asymptotically nonvanishing rate.