@article{LIU2009, 
author = {Haiyang LIU and Lianrong MA and Jie CHEN},
title = {Multistep Linear Programming Approaches for Decoding Low-Density Parity-Check Codes},
year = {2009},
journal = {Tsinghua Science and Technology},
volume = {14},
number = {5},
pages = {556-560},
keywords = {low-density parity-check (LDPC) codes, linear programming (LP), LP decoding, pseudocode-word, maximum-likelihood (ML) certificate property},
url = {https://www.sciopen.com/article/10.1016/S1007-0214(09)70117-8},
doi = {10.1016/S1007-0214(09)70117-8},
abstract = {The problem of improving the performance of linear programming (LP) decoding of low-density parity-check (LDPC) codes is considered in this paper. A multistep linear programming (MLP) algorithm was developed for decoding LDPC codes that includes a slight increase in computational complexity. The MLP decoder adaptively adds new constraints which are compatible with a selected check node to refine the results when an error is reported by the original LP decoder. The MLP decoder result is shown to have the maximum-likelihood (ML) certificate property. Simulations with moderate block length LDPC codes suggest that the MLP decoder gives better performance than both the original LP decoder and the conventional sum-product (SP) decoder.}
}