Performance analysis of linear codes under maximum-likelihood decoding: a tutorial
Communications and Information Theory
Capacity-achieving codes for finite-state channels with maximum-likelihood decoding
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Sharp bounds for optimal decoding of low-density parity-check codes
IEEE Transactions on Information Theory
On universal properties of capacity-approaching LDPC code ensembles
IEEE Transactions on Information Theory
Decay of correlations in low density parity check codes: low noise regime
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 4
Capacity-achieving codes for channels with memory with maximum-likelihood decoding
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
The generalized area theorem and some of its consequences
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Combinatorial approach to the interpolation method and scaling limits in sparse random graphs
Proceedings of the forty-second ACM symposium on Theory of computing
Tight bounds on the capacity of binary input random CDMA systems
IEEE Transactions on Information Theory
LT-codes and phase transitions for mutual information
ICITS'11 Proceedings of the 5th international conference on Information theoretic security
Unsatisfiability bounds for random CSPs from an energetic interpolation method
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
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A new method for analyzing low-density parity-check (LDPC) codes and low-density generator-matrix (LDGM) codes under bit maximum a posteriori probability (MAP) decoding is introduced. The method is based on a rigorous approach to spin glasses developed by Francesco Guerra. It allows one to construct lower bounds on the entropy of the transmitted message conditional to the received one. Based on heuristic statistical mechanics calculations, we conjecture such bounds to be tight. The result holds for standard irregular ensembles when used over binary-input output-symmetric (BIOS) channels. The method is first developed for Tanner-graph ensembles with Poisson left-degree distribution. It is then generalized to "multi-Poisson" graphs, and, by a completion procedure, to arbitrary degree distribution