Finding the Exhaustive List of Small Fully Absorbing Sets and Designing the Corresponding Low Error-Floor Decoder

• Published in: IEEE transactions on communications Vol. 60; no. 6; pp. 1487 - 1498
• Main Authors: Gyu Bum Kyung, Chih-Chun Wang
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.06.2012; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Branch-&-bound algorithms; Coding, codes; Complexity theory; Decoding; Equations; error floor; Exact sciences and technology; fully absorbing sets (FASs); Information, signal and communications theory; IP networks; Iterative decoding; low-density parity-check (LDPC) codes; Signal and communications theory; Telecommunications and information theory; Vectors; Error estimation; Branch and bound method; error floor; Decoding; fully absorbing sets (FASs); Search algorithm; Integer programming; Branch-&-bound algorithms; Credal approach; Algorithm performance; low-density parity-check (LDPC) codes; NP complete problem; Numerical simulation; Error correcting code; Parity check codes; Parity check
• ISSN: 0090-6778; 1558-0857
• DOI: 10.1109/TCOMM.2012.042712.100672

This work provides an efficient exhaustive search algorithm for finding all small fully absorbing sets (FASs) of any arbitrary low-density parity-check (LDPC) code. The proposed algorithm is based on the branch-&-bound principle for solving NP-complete problems. In particular, given any LDPC code, the problem of finding all FASs of size less than t is formulated as an integer programming problem, for which a new branch-&-bound algorithm is devised with new node selection and tree-trimming mechanisms. The resulting algorithm is capable of finding all FASs of size <; 7 for LDPC codes of length <; 1000. When limiting the FASs of interest to those with the number of violated parity-check nodes <; 3, the proposed algorithm is capable of finding all such FASs of size <; 14 for LDPC codes of lengths <; 1000. The resulting exhaustive list of small FASs is then used to devise a new efficient post-processing low-error floor LDPC decoder. The numerical results show that by exploiting the exhaustive list of small FASs, the proposed post-processing decoder can significantly lower the error-floor performance of a given LDPC code. For various example codes of length <; 3000, the proposed post-processing decoder lowers the error floor by a couple of orders of magnitude when compared to the standard belief propagation decoder and by an order of magnitude when compared to other existing low error-floor decoders.