Typical reconstruction limit of compressed sensing based on Lp-norm minimization (2009)
Kabashima, Y., Wadayama, T., Tanaka, T.
We consider the problem of reconstructing an $N$-dimensional continuous vector $\bx$ from $P$ constraints which are generated by its linear transformation under the assumption that the number of...
Regular and Irregular Gallager-type Error-Correcting Codes (2007)
Y. Kabashima, T. Murayama, D. Saad, R. Vicente
The performance of regular and irregular Gallager-type errorcorrecting code is investigated via methods of statistical physics. The transmitted codeword comprises products of the original message...
The polynomial error probability for LDPC codes (2003)
We obtain exact expressions for the asymptotic behaviour of the average probability of the block decoding error for ensembles of regular low density parity check error correcting codes, by employing...
Analysis of common attacks in LDPCC-based public-key cryptosystems (2003)
Skantzos, N. S., Saad, D., Kabashima, Y.
We analyze the security and reliability of a recently proposed class of public-key cryptosystems against attacks by unauthorized parties who have acquired partial knowledge of one or more of the...
Average and reliability error exponents in low-density parity-check codes (2003)
Skantzos, N. S., Van Mourik, J., Saad, D., Kabashima, Y.
We present a theoretical method for a direct evaluation of the average and reliability error exponents in low-density parity-check error-correcting codes using methods of statistical physics. Results...
Statistical mechanics of lossy data compression using a non-monotonic perceptron (2002)
Hosaka, T., Kabashima, Y., Nishimori, H.
The performance of a lossy data compression scheme for uniformly biased Boolean messages is investigated via methods of statistical mechanics. Inspired by a formal similarity to the storage capacity...
Critical Noise Levels for LDPC decoding (2002)
Van Mourik, J., Saad, D., Kabashima, Y.
We determine the critical noise level for decoding low density parity check error correcting codes based on the magnetization enumerator ($\cM$), rather than on the weight enumerator ($\cW$) employed...
Weight vs Magnetization Enumerator for Gallager Codes (2001)
Van Mourik, J., Saad, D., Kabashima, Y.
We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator ($\cM$),...
Belief propagation vs. TAP for decoding corrupted messages (1998)
PACS. 89.70+c – Information science. PACS. 89.90+n – Other areas of general interest to physicists. PACS. 02.50−r – Probability theory, stochastic processes, and statistics. Abstract. – We...