Low-density parity-check code: Difference between revisions

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Yet another way of constructing LDPC codes is to use [[finite geometry|finite geometries]]. This method was proposed by Y. Kou ''et al.'' in 2001.<ref name=Kou1>{{cite journal |first1=Y. |last1=Kou |first2=S. |last2=Lin |first3=M.P.C. |last3=Fossorier |title=Low-density parity-check codes based on finite geometries: a rediscovery and new results |journal=IEEE Transactions on Information Theory |volume=47 |issue=7 |pages=2711–36 |date=November 2001 |doi=10.1109/18.959255 }}</ref>
 
== LDPC codes vsVs. turbo codes ==
 
LDPC codes can be compared with other powerful coding schemes, e.g. [[turbo code]]s.<ref>{{cite conference |first1=B. |last1=Tahir |first2=S. |last2=Schwarz |first3=M. |last3=Rupp |title=BER comparison between Convolutional, Turbo, LDPC, and Polar codes |conference=2017 24th International Conference on Telecommunications (ICT), Limassol, Cyprus |volume= |issue= |pages=1–7 |date=2017 |doi=10.1109/ICT.2017.7998249 |url=}}</ref> In one hand, [[Bit error rate|BER]] performance of turbo codes is influenced by low codes limitations.<ref>{{cite book |first=K. |last=Moon Todd |title=Error correction coding: mathematical methods and algorithms |publisher=Wiley |___location= |date=2005 |isbn=0-471-64800-0 |pages=614 |url=}}</ref> LDPC codes have no limitations of minimum distance,<ref>{{harvnb|Moon Todd|2005|p=653}}</ref> that indirectly means that LDPC codes may be more efficient on relatively large [[code rate]]s (e.g. 3/4, 5/6, 7/8) than turbo codes. However, LDPC codes are not the complete replacement: turbo codes are the best solution at the lower code rates (e.g. 1/6, 1/3, 1/2).<ref>Andrews, Kenneth S., et al. "The development of turbo and LDPC codes for deep-space applications." Proceedings of the IEEE 95.11 (2007): 2142-2156.</ref><ref>Hassan, A.E.S., Dessouky, M., Abou Elazm, A. and Shokair, M., 2012. [https://www.researchgate.net/profile/Mona_Shokair/publication/234051399_Evaluation_of_Complexity_Versus_Performance_for_Turbo_Code_and_LDPC_Under_Different_Code_Rates/links/56b7b68908ae44bb330bc82f.pdf Evaluation of complexity versus performance for turbo code and LDPC under different code rates]. Proc. SPACOMM, pp.93-98.</ref>