Luby transform (LT) code[1]


Erasure codes based on fountain codes. They improve on random linear fountain codes by having a much more efficient encoding and decoding algorithm.

LT codes can be constructed as follows. First, randomly choose a degree \(d_n\) from a degree distribution depending on total size \(K\). Then, randomly choose \(d_n\) distinct source packets and let the packet to be transmitted \(\hat{p}_n\) be the bitwise sum of the chosen input packets. This forms a graph connecting encoded packets to source packets.


Sum-product algorithm, often called a peeling decoder [2][3], similar to belief propagation [4].


  • Raptor (RAPid TORnado) code — Raptor codes using a trivial pre-code are LT codes. Typically, Raptor codes have constant-sized more overhead but are faster to decode.

Zoo code information

Internal code ID: luby_transform

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Zoo Code ID: luby_transform

Cite as:
“Luby transform (LT) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.
@incollection{eczoo_luby_transform, title={Luby transform (LT) code}, booktitle={The Error Correction Zoo}, year={2022}, editor={Albert, Victor V. and Faist, Philippe}, url={} }
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M. Luby, “LT codes”, The 43rd Annual IEEE Symposium on Foundations of Computer Science, 2002. Proceedings.. DOI
T. Richardson and R. Urbanke, Modern Coding Theory (Cambridge University Press, 2008). DOI
David J. C. MacKay. 2002. Information Theory, Inference & Learning Algorithms. Cambridge University Press, USA
J. Pearl, “Reverend Bayes on Inference Engines: A Distributed Hierarchical Approach”, Probabilistic and Causal Inference 129 (2022). DOI

Cite as:

“Luby transform (LT) code”, The Error Correction Zoo (V. V. Albert & P. Faist, eds.), 2022.