Abstract
Since short cycles and trapping sets are culprits of performance and error floor of low-density parity-check (LDPC) codes, it is necessary to obtain information about the number and the distribution of all cycles in Tanner graphs. However, the established algorithms could not efficiently search all cycles on account of restrictions from both the structure and the girth of Tanner graphs. The proposed algorithm solve the above problems with message-passing schedule, counting and enumerating the cycles simultaneously. With information derived from the proposed algorithm, performance will be enhanced and error floor will be lower, which is meaningful for both adjustment and design of LDPC codes. Furthermore, the proposed algorithm can be applied on general bipartite graphs.
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References
Mao Y, Banihashemi AH (2001) A heuristic search for good low-density parity-check codes at short block lengths. Proc IEEE Int Conf Commun 1:41–44
Hu X-Y, Eleftheriou E, Arnold D-M (2001) Progressive edge-growth Tanner graphs. Proc IEEE Global Telecommun Conf 1:995–1001
Karimi M, Banihashemi AH (2012) Efficient algorithm for finding dominant trapping sets of LDPC codes. IEEE Trans Inf Theory 58(11):6942–6958
Xiao H, Banihashemi AH (2009) Error rate estimation of low-density parity-check codes on binary symmetric channels using cycle enumeration. IEEE Trans Commun 57(6):1550–1555
Asvadi R, Banihashemi AH, Ahmadian-Attari M (2011) Lowering the error floor of LDPC codes using cyclic liftings. IEEE Trans Inf Theory 57(4):2213–2224
Flum J, Grohe M (2002) The parameterized complexity of counting problems. Proc IEEE Symp Found Comput Sci 1:538–547
Tarjan R (1973) Enumeration of the elementary circuits of a directed graph. J SIAM 2:211–216
Johnson DB (1975) Find all the elementary circuits of a directed graph. J SIAM 4:77–84
Liu H, Wang J (2006) A new way to enumerate cycles in graph. In: Proceedings of the advanced international conference on telecommunications and international conference on internet and web applications and services (AICT/ICIW 2006)
Bax ET (1994) Algorithms to count paths and cycles. Inf Process Lett 52:249–252
Alon N, Yuster R, Zwick U (1997) Finding and counting given length cycles. Algorithmica 17(3):209–223
Fan J, Xiao Y (2006) A method of counting the number of cycles in LDPC codes. Proc Int Conf Signal Process 3:2183–2186
Chen R, Huang H, Xiao G (2007) Relation between parity-check matrices and cycles of as-sociated Tanner graphs. IEEE Commun Lett 11(8):674–676
Halford TR, Chugg KM (2006) An algorithm for counting short cycles in bipartite graphs. IEEE Trans Inf Theory 52(1):287–292
Karimi M, Banihashemi AH (2013) Message-passing algorithms for counting short cycles in a graph. IEEE Trans Commun 61(2):485–495
D. MacKay’s Gallager Code Resources [Online]. http://www.inference.phy.cam.ac.uk/mackay/codes/
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Yang, K., Zhang, B., Zhan, Y., Guo, D. (2017). Design and Analysis of Efficient Algorithm for Counting and Enumerating Cycles in LDPC Codes. In: Balas, V., Jain, L., Zhao, X. (eds) Information Technology and Intelligent Transportation Systems. Advances in Intelligent Systems and Computing, vol 454. Springer, Cham. https://doi.org/10.1007/978-3-319-38789-5_23
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DOI: https://doi.org/10.1007/978-3-319-38789-5_23
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