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A `!Sparse graph code`! is a `F33f`_`[code`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Code]`_`f which is represented by a `F33f`_`[sparse graph`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Sparse_graph]`_`f.

Any `F33f`_`[linear code`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Linear_code]`_`f can be represented as a graph, where there are two sets of nodes - a set representing the transmitted `F33f`_`[bits`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Bit]`_`f and another set representing the constraints that the transmitted bits have to satisfy. The state of the art classical `F33f`_`[error-correcting codes`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Error-correcting_code]`_`f are based on sparse graphs, achieving close to the `F33f`_`[Shannon limit`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Shannon_limit]`_`f. The archetypal sparse-graph codes are `F33f`_`[Gallager's`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Robert_G._Gallager]`_`f `F33f`_`[low-density parity-check codes`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=Low-density_parity-check_code]`_`f.

>>External links

• The on-line textbook: Information Theory, Inference, and Learning Algorithms, by `F33f`_`[David J.C. MacKay`:/page/wikibook/entry.mu`zim=wikipedia_en_all_nopic_2025-08.zim|entry_path=David_J.C._MacKay]`_`f, discusses sparse-graph codes in Chapters 47–50.

• Encyclopedia of Sparse Graph Codes

• Iterative Error Correction: Turbo, Low-Density Parity-Check, and Repeat-Cccumulate Codes

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