Towards Low-Complexity Linear-Programming Decoding
<|reference_start|>Towards Low-Complexity Linear-Programming Decoding: We consider linear-programming (LP) decoding of low-density parity-check (LDPC) codes. While it is clear that one can use any general-purpose LP solver to solve the LP that appears in the decoding problem, we argue in this paper that the LP at hand is equipped with a lot of structure that one should take advantage of. Towards this goal, we study the dual LP and show how coordinate-ascent methods lead to very simple update rules that are tightly connected to the min-sum algorithm. Moreover, replacing minima in the formula of the dual LP with soft-minima one obtains update rules that are tightly connected to the sum-product algorithm. This shows that LP solvers with complexity similar to the min-sum algorithm and the sum-product algorithm are feasible. Finally, we also discuss some sub-gradient-based methods.<|reference_end|>
@article{vontobel2006towards,
    title={Towards Low-Complexity Linear-Programming Decoding},
    author={Pascal O. Vontobel and Ralf Koetter},
    journal={Proc. 4th Int. Symposium on Turbo Codes and Related Topics,
  Munich, Germany, April 3-7, 2006},
    year={2006},
    archivePrefix={arXiv},
    eprint={cs/0602088},
    primaryClass={cs.IT math.IT}
}