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LDPC codes are a class of [[Error correction code|error correction codes]] which (together with the closely-related [[Turbo code|turbo codes]]) have gained prominence in [[coding theory]] and [[information theory]] in the late 1990s. The codes today are widely used in applications ranging from wireless communications to flash-memory storage. Together with turbo codes, they sparked a revolution in coding theory, achieving order-of-magnitude improvements in performance compared to traditional error correction codes<ref>{{Cite web |title=Turbo Codes Explained: History, Examples, and Applications - IEEE Spectrum |url=https://spectrum.ieee.org/turbo-codes |access-date=2024-12-18 |website=spectrum.ieee.org |language=en}}</ref>.
Theoretically, sequences of LDPC codes exist at rates that approach theoretical limits ([[Channel capacity|capacities]]) of many channels<ref>{{Cite web |title=Design of capacity-approaching irregular low-density parity-check codes |url=https://ieeexplore.ieee.org/document/910578 |archive-url=http://web.archive.org/web/20240909161749/https://ieeexplore.ieee.org/document/910578/ |archive-date=2024-09-09 |access-date=2024-12-18 |website=ieeexplore.ieee.org |language=en-US}}</ref>. Codes within each such sequence, have increasing block length (at the same [[code rate]]). Most importantly, when appropriately designed, the codes in the sequence can be decoded using
This theoretical performance is made possible using a flexible design method that is based on sparse [[Tanner graph|Tanner graphs]] (specialized [[bipartite graph|bipartite graphs]]).<ref>{{citation |author=Amin Shokrollahi |url=http://www.ics.uci.edu/~welling/teaching/ICS279/LPCD.pdf |title=LDPC Codes: An Introduction |archive-url=https://web.archive.org/web/20170517034849/http://www.ics.uci.edu/~welling/teaching/ICS279/LPCD.pdf |archive-date=2017-05-17}}</ref>
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