BCJR algorithm

The Bahl-Cocke-Jelinek-Raviv (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 $$\alpha$$
 * Compute backward probabilities $$\beta$$
 * 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++.