Monotonic optimization based decoding for linear codes

• Published in: Journal of global optimization Vol. 55; no. 2; pp. 301 - 312
• Main Authors: Tuan, H. D., Son, T. T., Tuy, H., Khoa, P. T.
• Format: Journal Article
• Language: English
• Published: Boston Springer US 01.02.2013; Springer; Springer Nature B.V
• Subjects: Algorithms; Channels; Codes; Computer Science; Computer simulation; Decoding; Gaussian; Iterative methods; Linear codes; Linear programming; Low density parity check codes; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Operations Research/Decision Theory; Optimization; Real Functions; Studies; Linear codes; Global optimization; Low density parity check (LDPC) codes; Maximum likelihood decoding
• ISSN: 0925-5001; 1573-2916
• DOI: 10.1007/s10898-011-9816-9

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.