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The '''BCJR algorithm''' is an algorithm for [[maximum a posteriori]] decoding of [[error correcting code]]s defined on trellises (principally [[convolutional code]]s). The algorithm is named after its inventors: Bahl, Cocke, [[Frederick Jelinek|Jelinek]] and Raviv. This algorithm is critical to modern iteratively-decoded error-correcting codes including [[turbo code]]s and [[low-density parity-check code]]s.

==Steps involved==
Based on the [[convolutional code|trellis]]:

* Compute forward probabilities <math>\alpha</math>
* Compute backward probabilities <math>\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.

===Log-Map BCJR===

===Max-Log-Map BCJR ===

==Implementations==
* [http://susalib.org/ Susa] framework implements BCJR algorithm for [[forward error correction]] codes and channel equalization in C++.

==See also==
* [[Forward-backward algorithm]]
* [[Maximum a posteriori|Maximum a posteriori (MAP) estimation]]
* [[Hidden Markov model]]

==External links==
* [http://www.inference.phy.cam.ac.uk/mackay/itila/ The online textbook: Information Theory, Inference, and Learning Algorithms], by [[David J.C. MacKay]], discusses the BCJR algorithm in chapter 25.
* [https://github.com/behrooza/susa/blob/master/inc/susa/channel.h#L360 The implementation of BCJR algorithm in Susa signal processing framework]

==Source==

[http://wikipedia.org/ http://wikipedia.org/]

BCJR algorithm - Revision history

Admin: Created page with "The '''BCJR algorithm''' is an algorithm for maximum a posteriori decoding of error correcting codes defined on trellises (principally convolutional codes). The al..."