BCJR algorithm
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Short description: Error correction algorithm
The BCJR algorithm is an algorithm for maximum a posteriori decoding of error correcting codes defined on trellises (principally convolutional codes). The algorithm is named after its inventors: Bahl, Cocke, Jelinek and Raviv.[1] This algorithm is critical to modern iteratively-decoded error-correcting codes, including turbo codes and low-density parity-check codes.
Steps involved
Based on the trellis:
- Compute forward probabilities [math]\displaystyle{ \alpha }[/math]
- Compute backward probabilities [math]\displaystyle{ \beta }[/math]
- Compute smoothed probabilities based on other information (i.e. noise variance for AWGN, bit crossover probability for binary symmetric channel)
Variations
SBGT BCJR
Berrou, Glavieux and Thitimajshima simplification.[2]
Log-Map BCJR
Implementations
- Susa framework implements BCJR algorithm for forward error correction codes and channel equalization in C++.
See also
- Forward-backward algorithm
- Maximum a posteriori (MAP) estimation
- Hidden Markov model
References
- ↑ Bahl, L.; Cocke, J.; Jelinek, F.; Raviv, J. (March 1974). "Optimal Decoding of Linear Codes for minimizing symbol error rate". IEEE Transactions on Information Theory 20 (2): 284–7. doi:10.1109/TIT.1974.1055186.
- ↑ Wang, Sichun; Patenaude, François (2006). "A Systematic Approach to Modified BCJR MAP Algorithms for Convolutional Codes". EURASIP Journal on Applied Signal Processing 2006: 95360. doi:10.1155/ASP/2006/95360. Bibcode: 2006EJASP2006..242W.
- ↑ Robertson, P.; Hoeher, P.; Villebrun, E. (1997). "Optimal and Sub-Optimal Maximum A Posteriori Algorithms Suitable for Turbo Decoding". European Transactions on Telecommunications 8 (2): 119–125. doi:10.1002/ett.4460080202.
External links
- The online textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay, discusses the BCJR algorithm in chapter 25.
- The implementation of BCJR algorithm in Susa signal processing framework
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