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BCJR algorithm

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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.

Contents

Steps involved

Based on the trellis:

  • Compute forward probabilities α
  • Compute backward probabilities β
  • Compute smoothed probabilities based on other information (i.e. noise variance for AWGN, bit crossover probability for binary symmetric channel)

    • SBGT BCJR

    Berrou, Glavieux and Thitimajshima simplification.

    Implementations

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

    • References

    BCJR algorithm Wikipedia
    (Text) CC BY-SA