Applying Bayesian networks and belief propagation to error correction coding

Telecommunication standards utilise numerous different subsystems to improve the quality of voice and data communications. One of these subsystems is tasked with error detection and control within the transmitted streams. This is accomplished using numerous different error correction codes for various scenarios. This article investigates the use of a Bayesian network as a universal channel decoder for the two main branches of algebraic codes. This graph-based approach is visually intuitive and is found to produce similar results to the best performing decoders in use today. A graphical representation of a multi-path channel equaliser is incorporated into the Bayesian network, obtaining near optimal performance. References G. Colavolpe. On LDPC codes over channels with memory. IEEE T. Wirel. Commun., 5(7):1757–1766, 2006. doi:10.1109/TWC.2006.1673087. C. Douillard, M. Jezequel, C. Berrou, A. Picart, P. Didier, and A. Glavieux. Iterative correction of intersymbol interference: Turbo-equalization. Eur. T. Telecommun., 6(5):507–511, 1995. doi:10.1002/ett.4460060506. R. G. Gallager. Low-density parity-check codes. PhD thesis, Massachusetts Institute of Technology, 1963. http://www.rle.mit.edu/rgallager/documents/ldpc.pdf. R. J. McEliece, D. J. C. MacKay, and J.-F. Cheng. Turbo decoding as an instance of Pearl's ``belief propagation'' algorithm. IEEE J. Sel. Area. Comm., 16(2):140–152, 1998. doi:10.1109/49.661103 H. C. Myburgh, J. C Olivier, and A. J. van Zyl. Reduced complexity turbo equalization using a dynamic bayesian network. EURASIP J. Adv. Sig. Pr., 2012:136, 2012. doi:10.1186/1687-6180-2012-136. J. Pearl. Fusion, propagation, and structuring in belief networks. Artif. Intell., 29(3):241–288, 1986. doi:10.1016/0004-3702(86)90072-X. J. Pearl. Probabilistic reasoning in intelligent systems: networks of plausible inference. Morgan Kaufmann Publishers, 1988. J. G. Proakis and D. G. Manolakis. Digital communications McGraw-Hill New York, 1995. International Telecommunication Union. Requirements related to technical performance for IMT-Advanced radio interface(s). Technical report, http://www.itu.int/pub/R-REP-M.2134-2008, 2008. A. J. Viterbi. Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE T. Inform. Theory, 13(2):260–269, 1967. doi:10.1109/TIT.1967.1054010