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Improved Linear Programming Decoding of LDPC Codes and Bounds on the Minimum and Fractional Distance

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2 Author(s)
Burshtein, D. ; Sch. of Electr. Eng., Tel-Aviv Univ., Tel-Aviv, Israel ; Goldenberg, I.

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.

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Information Theory, IEEE Transactions on  (Volume:57 ,  Issue: 11 )