Monotonic optimization based decoding for linear codes
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...
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| Published in | Journal of global optimization Vol. 55; no. 2; pp. 301 - 312 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Boston
Springer US
01.02.2013
Springer Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0925-5001 1573-2916 |
| DOI | 10.1007/s10898-011-9816-9 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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.[PUBLICATION ABSTRACT] 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. Keywords Linear codes * Low density parity check (LDPC) codes * Maximum likelihood decoding * Global optimization 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. |
| Audience | Academic |
| Author | Tuan, H. D. Tuy, H. Son, T. T. Khoa, P. T. |
| Author_xml | – sequence: 1 givenname: H. D. surname: Tuan fullname: Tuan, H. D. email: tuan.hoang@uts.edu.au organization: Faculty of Engineering and Information Technology, University of Technology – sequence: 2 givenname: T. T. surname: Son fullname: Son, T. T. organization: Department of Computer Vision and Robotics-FIT, University of Science – sequence: 3 givenname: H. surname: Tuy fullname: Tuy, H. organization: Institute of Mathematics – sequence: 4 givenname: P. T. surname: Khoa fullname: Khoa, P. T. organization: Department of Electrical Engineering, University of California in Los Angeles (UCLA) |
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| Cites_doi | 10.1109/TIT.1981.1056404 10.1109/TIT.2004.842696 10.1109/JSAC.2006.879405 10.1109/49.661103 10.1109/TIT.2005.850085 10.1049/el:19961141 10.1007/BF01096415 10.1137/04060932X 10.1162/08997660260028674 10.1016/S0377-0427(00)00425-8 10.1002/nav.3800030109 10.1007/BF02579283 10.1109/18.910572 10.1137/S1052623499359828 10.1109/TIT.1978.1055873 10.1109/18.748992 10.1109/TIT.1962.1057683 |
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| DOI | 10.1007/s10898-011-9816-9 |
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| Keywords | Linear codes Global optimization Low density parity check (LDPC) codes Maximum likelihood decoding |
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| References | Tuy (CR15) 1999 McEliece, MacKay, Cheng (CR11) 1998; 16 Yedidia, Freeman, Weiss (CR20) 2005; 51 Tanner (CR14) 1981; 27 Tuy (CR17) 2000; 11 Kschischang, Frey, Loeliger (CR6) 2001; 47 CR7 Margulis (CR10) 1982; 2 Yang, Feldman, Wang (CR18) 2006; 24 Tuy, Minoux, Phuong (CR16) 2006; 17 Yedidia, Freeman, Weiss, Lakemeyer, Nebel (CR19) 2003 Mackay (CR9) 1999; 45 Berlekamp, McElice, van Tiborg (CR1) 1978; 24 Mackay, Neal (CR8) 1996; 32 Pearl (CR13) 1988 Feldman, Wainwright, Karger (CR2) 2005; 51 Frank, Wolfe (CR3) 1956; 3 Yuille (CR21) 2002; 14 Hasselberg, Pardalos, Vairaktarakis (CR5) 1993; 3 Pardalos, Romeijn, Tuy (CR12) 2000; 124 Gallager (CR4) 1962 K. Yang (9816_CR18) 2006; 24 R.M. Tanner (9816_CR14) 1981; 27 J.S. Yedidia (9816_CR20) 2005; 51 H. Tuy (9816_CR17) 2000; 11 J.S. Yedidia (9816_CR19) 2003 H. Tuy (9816_CR15) 1999 D.J.C. Mackay (9816_CR8) 1996; 32 E.R. Berlekamp (9816_CR1) 1978; 24 R. McEliece (9816_CR11) 1998; 16 9816_CR7 G.A. Margulis (9816_CR10) 1982; 2 R.G. Gallager (9816_CR4) 1962 J. Hasselberg (9816_CR5) 1993; 3 F.R. Kschischang (9816_CR6) 2001; 47 J. Pearl (9816_CR13) 1988 P.M. Pardalos (9816_CR12) 2000; 124 J. Feldman (9816_CR2) 2005; 51 D.J.C. Mackay (9816_CR9) 1999; 45 H. Tuy (9816_CR16) 2006; 17 A.L. Yuille (9816_CR21) 2002; 14 M. Frank (9816_CR3) 1956; 3 |
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| SubjectTerms | 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 |
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| Title | Monotonic optimization based decoding for linear codes |
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