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
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
Absdet-pseudo-codewords and perm-pseudo-codewords: definitions and properties
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
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
Ensemble pseudocodeword weight enumerators for protograph-based generalized LDPC codes
GLOBECOM'09 Proceedings of the 28th IEEE conference on Global telecommunications
| Hi-index | 754.90 |
In linear programming (LP) decoding of a low-density parity-check (LDPC) code one minimizes a linear functional, with coefficients related to log-likelihood ratios, over a relaxation of the polytope spanned by the codewords. In order to quantify LP decoding it is important to study vertexes of the relaxed polytope, so-called pseudocodewords. We propose a technique to heuristcally create a list of pseudocodewords close to the zero codeword and their distances. Our pseudocodeword-search algorithm starts by randomly choosing configuration of the noise. The configuration is modified through a discrete number of steps. Each step consists of two substeps: one applies an LP decoder to the noise-configuration deriving a pseudocodeword, and then finds configuration of the noise equidistant from the pseudocodeword and the zero codeword. The resulting noise configuration is used as an entry for the next step. The iterations converge rapidly to a pseudocodeword neighboring the zero codeword. Repeated many times, this procedure is characterized by the distribution function of the pseudocodeword effective distance. The efficiency of the procedure is demonstrated on examples of the Tanner code and Margulis codes operating over an additive white Gaussian noise (AWGN) channel.