Low-density parity-check code: Difference between revisions

Revision as of 19:55, 18 December 2024

Revision as of 21:59, 18 December 2024

Line 5:

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,Central sequencesto the performance of LDPC codes existis attheir ratesadaptability thatto the iterative [[belief propagation]] decoding algorithm, under which they were shown to 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>. at Codeslow withincomputation eachcost. such sequenceTheoretically, haveanalysis increasingof blockthe lengthcodes (atfocuses theon samesequences of codes of fixed [[code rate]]). and Mostincreasing importantly,[[block whenlength]]. appropriately designed,When considering the decoding of codes in the sequence canunder bebelief decodedpropagation, usingin anmany iterativecase [[beliefthe propagation]]decoding algorithm,error can be proven to achievebe vanishingly small decoding(approaches errorzero with the block length), at a complexity that is linear in the block length.

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>