TheBahl-Cocke-Jelinek-Raviv (BCJR) algorithm is analgorithm formaximum a posteriori decoding oferror correcting codes defined ontrellises (principallyconvolutional 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, includingturbo codes andlow-density parity-check codes.

Based on thetrellis:

• Compute forward probabilities${\displaystyle \alpha }$
• Compute backward probabilities${\displaystyle \beta }$
• Compute smoothed probabilities based on other information (i.e.noise variance forAWGN,bit crossover probability forbinary symmetric channel)

Berrou, Glavieux and Thitimajshima simplification.^[2]

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^[3]

• Susa framework implements BCJR algorithm forforward error correction codes and channel equalization in C++.

• Forward-backward algorithm
• Maximum a posteriori (MAP) estimation
• Hidden Markov model

• The online textbook: Information Theory, Inference, and Learning Algorithms, byDavid J.C. MacKay, discusses the BCJR algorithm in chapter 25.
• The implementation of BCJR algorithm in Susa signal processing framework

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