TY - JOUR
T1 - Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance
AU - Burshtein, David
AU - Goldenberg, Idan
N1 - Funding Information:
Manuscript received November 23, 2010; revised April 03, 2011; accepted July 07, 2011. Date of current version November 11, 2011. This work was supported by the Israel Science Foundation under Grant 772/09. The material in this paper was presented in part at the 2010 Information Theory Workshop, Dublin, Ireland, and at the 2011 IEEE International Symposium on Information Theory. The authors are with the School of Electrical Engineering, Tel-Aviv University, Tel-Aviv 69978, Israel (e-mail: burstyn@eng.tau.ac.il; idang@eng.tau.ac. il). Communicated by E. Arikan, Associate Editor for Coding Techniques. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2011.2162224
PY - 2011/11
Y1 - 2011/11
N2 - We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an algorithm which calculates a lower bound on the minimum distance of a specific code. This algorithm exhibits complexity which scales quadratically with the block length. Third, we propose a method to obtain a tight lower bound on the fractional distance, also with quadratic complexity, and thus less than previously-existing methods. Finally, we show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained.
AB - We examine LDPC codes decoded using linear programming (LP). Four contributions to the LP framework are presented. First, a new method of tightening the LP relaxation, and thus improving the LP decoder, is proposed. Second, we present an algorithm which calculates a lower bound on the minimum distance of a specific code. This algorithm exhibits complexity which scales quadratically with the block length. Third, we propose a method to obtain a tight lower bound on the fractional distance, also with quadratic complexity, and thus less than previously-existing methods. Finally, we show how the fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can be obtained.
KW - Fractional distance
KW - linear programming decoding
KW - low-density parity-check (LDPC) codes
KW - maximum likelihood (ML) decoding
KW - minimum distance
UR - http://www.scopus.com/inward/record.url?scp=81255143080&partnerID=8YFLogxK
U2 - 10.1109/TIT.2011.2162224
DO - 10.1109/TIT.2011.2162224
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AN - SCOPUS:81255143080
VL - 57
SP - 7386
EP - 7402
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
SN - 0018-9448
IS - 11
M1 - 5955120
ER -