References

Here are some papers and other resources that were helpful for understanding protograph LDPC codes and implementing this library.

Table of Contents

• Papers
• Software
• Learning material

Papers

LDPC codes

• Gallager, Robert. “Low-density parity-check codes.” IRE Transactions on information theory 8.1 (1962): 21-28.
• Hu, Xiao-Yu, Evangelos Eleftheriou, and Dieter-Michael Arnold. “Regular and irregular progressive edge-growth tanner graphs.” IEEE Transactions on Information Theory 51.1 (2005): 386-398.
• MacKay, David JC. “Good error-correcting codes based on very sparse matrices.” IEEE transactions on Information Theory 45.2 (1999): 399-431.
• MacKay, David JC, and Radford M. Neal. “Near Shannon limit performance of low density parity check codes.” Electronics letters 32.18 (1996): 1645-1646.

Protograph LDPC codes

• Divsalar, Dariush, Sam Dolinar, and Christopher Jones. “Construction of protograph LDPC codes with linear minimum distance.” 2006 IEEE International Symposium on Information Theory. IEEE, 2006.
• Fang, Yi, et al. “A survey on protograph LDPC codes and their applications.” IEEE Communications Surveys & Tutorials 17.4 (2015): 1989-2016.
• Thorpe, Jeremy. “Low-density parity-check (LDPC) codes constructed from protographs.” IPN progress report 42.154 (2003): 42-154.

Other

• Butler, Brian K., and Paul H. Siegel. “Bounds on the minimum distance of punctured quasi-cyclic LDPC codes.” IEEE transactions on information theory 59.7 (2013): 4584-4597.
• Chandak, Shubham, et al. “Improved read/write cost tradeoff in DNA-based data storage using LDPC codes.” 2019 57th Annual Allerton Conference on Communication, Control, and Computing (Allerton). IEEE, 2019.
• Mitchell, David GM, Roxana Smarandache, and Daniel J. Costello. “Quasi-cyclic LDPC codes based on pre-lifted protographs.” IEEE Transactions on Information Theory 60.10 (2014): 5856-5874.
• Van Nguyen, Thuy, Aria Nosratinia, and Dariush Divsalar. “The design of rate-compatible protograph LDPC codes.” IEEE Transactions on communications 60.10 (2012): 2841-2850.

Software

• Software for Low Density Parity Check Codes:
  • https://shubhamchandak94.github.io/LDPC-codes/
  • http://radfordneal.github.io/LDPC-codes/
• Source code for Progressive Edge Growth parity-check matrix construction:
  • http://www.inference.org.uk/mackay/PEG_ECC.html

Learning material

• Introduction to Error-Correcting Codes (Mary Wootters, EE 25N, Stanford): [YouTube]
• Error Correcting Codes playlist (eigenchris): [YouTube]
• Hamming & low density parity check codes (Art of the Problem): [YouTube]
• Hamming codes and error correction (2 video series on YouTube): [part 1][part 2]
• LDPC Codes - a brief Tutorial (Bernhard M.J. Leiner): [pdf]
• LDPC and Polar Codes in 5G Standard playlist (Andrew Thangaraj, IIT Madras): [YouTube]
• EE 388 course material (Andrea Montanari, Stanford): [Website]
• Wikipedia pages on Error correction codes, Linear codes and LDPC codes.

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