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. 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
Compute backward probabilities
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.
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
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