Tanner code[1] 

Also known as Generalized LDPC (GLDPC) code.


A linear \(q\)-ary code defined on a bipartite graph similar to a Tanner graph. This generalized Tanner graph consists of variable nodes and constraint nodes, with the generalization being that the constraint nodes of degree \(r\) now represent a linear codes of length \(r\).

A string is in the Tanner code if all substrings satisfy their corresponding constraints, i.e., all substrings are members of the linear codes represented on the constraint nodes.

A code is called regular if the corresponding bipartite graph is regular. Expansion properties of the underlying graph can yield efficient decoding algorithms.


Min-sum and sum-product iterative decoders for binary Tanner codes [2,3]; see also [4,5]. These decoders can be improved using a probabilistic message-passing schedule [6].Any code can be put into normal form without significantly altering the underlying graph or the decoding complexity [7]. For an algebraic viewpoint on decoding, see [8].Iterative decoding is optimal for Tanner graphs that are free of cycles [3]. However, codes that admit cycle-free representations have bounds on their distances [1,9]; see [10,11].



  • Regular binary Tanner code — Regular binary Tanner codes are binary Tanner codes defined on regular sparse bipartite graphs, with the inner code being the same for all vertices.
  • \(q\)-ary LDPC code — \(q\)-ary LDPC codes are \(q\)-ary Tanner codes on sparse bipartite graphs whose constraint nodes represent \(q\)-ary parity-check codes.


  • Expander LP code — Expander lifted-product codes are products of regular \(q\)-ary Tanner codes defined on expander graphs [12].


R. Tanner, “A recursive approach to low complexity codes”, IEEE Transactions on Information Theory 27, 533 (1981) DOI
N. Wiberg, H.-A. Loeliger, and R. Kotter, “Codes and iterative decoding on general graphs”, European Transactions on Telecommunications 6, 513 (1995) DOI
Niclas Wiberg, Codes and decoding on general graphs. 1996. PhD thesis, Linköping University, Linköping, Sweden
Brendan J. Frey. Graphical models for machine learning and digital communication. MIT press, 1998.
R. McEliece, The Theory of Information and Coding (Cambridge University Press, 2002) DOI
Yongyi Mao and A. H. Banihashemi, “Decoding low-density parity-check codes with probabilistic schedule”, 2001 IEEE Pacific Rim Conference on Communications, Computers and Signal Processing (IEEE Cat. No.01CH37233) DOI
G. D. Forney, “Codes on graphs: normal realizations”, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060) DOI
E. Soljanin and E. Offer, “LDPC codes: a group algebra formulation”, Electronic Notes in Discrete Mathematics 6, 148 (2001) DOI
T. Etzion, A. Trachtenberg, and A. Vardy, “Which codes have cycle-free Tanner graphs?”, IEEE Transactions on Information Theory 45, 2173 (1999) DOI
C. A. Kelley, "Codes over Graphs." Concise Encyclopedia of Coding Theory (Chapman and Hall/CRC, 2021) DOI
D. K. Kythe and P. K. Kythe, “Algebraic and Stochastic Coding Theory”, (2017) DOI
S. Hoory, N. Linial, and A. Wigderson, “Expander graphs and their applications”, Bulletin of the American Mathematical Society 43, 439 (2006) DOI
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Zoo Code ID: tanner

Cite as:
“Tanner code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/tanner
@incollection{eczoo_tanner, title={Tanner code}, booktitle={The Error Correction Zoo}, year={2023}, editor={Albert, Victor V. and Faist, Philippe}, url={https://errorcorrectionzoo.org/c/tanner} }
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Cite as:

“Tanner code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2023. https://errorcorrectionzoo.org/c/tanner

Github: https://github.com/errorcorrectionzoo/eczoo_data/edit/main/codes/classical/q-ary_digits/tanner/tanner.yml.