Performance analysis of linear codes under maximum-likelihood decoding: a tutorial
Communications and Information Theory
An FPGA implementation of (3, 6)-regular low-density parity-check code decoder
EURASIP Journal on Applied Signal Processing
Performance of Standard Irregular LDPC Codes under Maximum Likelihood Decoding
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Construction of Universal Codes Using LDPC Matrices and Their Error Exponents
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A Construction of Lossy Source Code Using LDPC Matrices
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
An Application of Linear Codes to the Problem of Source Coding with Partial Side Information
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Capacity-achieving codes for finite-state channels with maximum-likelihood decoding
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
The capacity of finite Abelian group codes over symmetric memoryless channels
IEEE Transactions on Information Theory
Upper bound on error exponent of regular LDPC codes transmitted over the BEC
IEEE Transactions on Information Theory
Variable length lossy coding using an LDPC code
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 3
Coding theorem for general stationary memoryless channel based on hash property
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
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
Performance bounds for nonbinary linear block codes over memoryless symmetric channels
IEEE Transactions on Information Theory
Hash property and coding theorems for sparse matrices and maximum-likelihood coding
IEEE Transactions on Information Theory
Capacity-achieving codes with bounded graphical complexity and maximum likelihood decoding
IEEE Transactions on Information Theory
Hybrid channel codes for efficient FSO/RF communication systems
IEEE Transactions on Communications
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We derive both upper and lower bounds on the decoding error probability of maximum-likelihood (ML) decoded low-density parity-check (LDPC) codes. The results hold for any binary-input symmetric-output channel. Our results indicate that for various appropriately chosen ensembles of LDPC codes, reliable communication is possible up to channel capacity. However, the ensemble averaged decoding error probability decreases polynomially, and not exponentially. The lower and upper bounds coincide asymptotically, thus showing the tightness of the bounds. However, for ensembles with suitably chosen parameters, the error probability of almost all codes is exponentially decreasing, with an error exponent that can be set arbitrarily close to the standard random coding exponent