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
Pseudocodeword performance analysis for LDPC convolutional codes
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
FPGA-based low-complexity high-throughput tri-mode decoder for quasi-cyclic LDPC codes
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Spectral graph analysis of quasi-cyclic codes
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
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We consider coded data transmission over a binary-input output-symmetric memoryless channel using a binary linear code. In order to understand the performance of maximum-likelihood (ML) decoding, one studies the codewords, in particular the minimal codewords, and their Hamming weights. In the context of linear programming (LP) decoding, one's attention needs to be shifted to the pseudo-codewords, in particular, to the minimal pseudo-codewords and their pseudo-weights. In this paper, we investigate some families of codes that have good properties under LP decoding, namely certain families of low-density parity-check (LDPC) codes that are derived from projective and Euclidean planes: we study the structure of their minimal pseudo-codewords and give lower bounds on their pseudo-weight. Besides this main focus, we also present some results that hold for pseudo-codewords and minimal pseudo-codewords of any Tanner graph, and we highlight how the importance of minimal pseudo-codewords under LP decoding varies depending on which binary-input output-symmetric memoryless channel is used.