Journal of Global Optimization

, Volume 55, Issue 2, pp 301–312 | Cite as

Monotonic optimization based decoding for linear codes

  • H. D. TuanEmail author
  • T. T. Son
  • H. Tuy
  • P. T. Khoa


New efficient methods are developed for the optimal maximum-likelihood (ML) decoding of an arbitrary binary linear code based on data received from any discrete Gaussian channel. The decoding algorithm is based on monotonic optimization that is minimizing a difference of monotonic (d.m.) objective functions subject to the 0–1 constraints of bit variables. The iterative process converges to the global optimal ML solution after finitely many steps. The proposed algorithm’s computational complexity depends on input sequence length k which is much less than the codeword length n, especially for a codes with small code rate. The viability of the developed is verified through simulations on different coding schemes.


Linear codes Low density parity check (LDPC) codes Maximum likelihood decoding Global optimization 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Faculty of Engineering and Information TechnologyUniversity of TechnologySydneyAustralia
  2. 2.Department of Computer Vision and Robotics-FITUniversity of ScienceHochiminh CityVietnam
  3. 3.Institute of MathematicsHanoiVietnam
  4. 4.Department of Electrical EngineeringUniversity of California in Los Angeles (UCLA)Los AngelesUSA

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