Instanton-based techniques for analysis and reduction of error floors of LDPC codes
IEEE Journal on Selected Areas in Communications - Special issue on capaciyy approaching codes
Improved random redundant iterative HDPC decoding
IEEE Transactions on Communications
IEEE Transactions on Information Theory
Analysis of connections between pseudocodewords
IEEE Transactions on Information Theory
Single-exclusion number and the stopping redundancy of MDS codes
IEEE Transactions on Information Theory
On Linear Programming Decoding on a Quantized Additive White Gaussian Noise Channel
Cryptography and Coding '09 Proceedings of the 12th IMA International Conference on Cryptography and Coding
Analysis of error floors of LDPC codes under LP decoding over the BSC
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Minimum distance and pseudodistance lower bounds for generalised LDPC codes
International Journal of Information and Coding Theory
LP decoding meets LP decoding: a connection between channel coding and compressed sensing
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Ensemble pseudocodeword weight enumerators for protograph-based generalized LDPC codes
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
Multiple-bases belief-propagation decoding of high-density cyclic codes
IEEE Transactions on Communications
| Hi-index | 755.02 |
This paper presents a detailed analysis of pseudocodewords of Tanner graphs. Pseudocodewords arising on the iterative decoder's computation tree are distinguished from pseudocodewords arising on finite degree lifts. Lower bounds on the minimum pseudocodeword weight are presented for the BEC, BSC, and AWGN channel. Some structural properties of pseudocodewords are examined, and pseudocodewords and graph properties that are potentially problematic with min-sum iterative decoding are identified. An upper bound on the minimum degree lift needed to realize a particular irreducible lift-realizable pseudocodeword is given in terms of its maximal component, and it is shown that all irreducible lift-realizable pseudocodewords have components upper bounded by a finite value t that is dependent on the graph structure. Examples and different Tanner graph representations of individual codes are examined and the resulting pseudocodeword distributions and iterative decoding performances are analyzed. The results obtained provide some insights in relating the structure of the Tanner graph to the pseudocodeword distribution and suggest ways of designing Tanner graphs with good minimum pseudocodeword weight.