This tutorial paper reviews the basics of error correcting codes like linear block codes and LDPC. The error correcting codes which are also known as channel codes enable to recover the original message from the message that has been corrupted by the noisy channel. These block codes can be graphically represented by
factor graphs. We mention the link between factor graphs, graphical models like Bayesian networks, channel coding and compressive sensing. In this paper, we discuss an iterative decoding algorithm called Message Passing Algorithm that operates in factor graph, and compute the marginal function associated with the global function of the variables. This global function is factorized into many simple local functions which are defined by parity check matrix of the code. We also discuss the role of Message Passing Algorithm in Compressive Sensing reconstruction of sparse signal.
K. Sunil, Soman, K. P., and Jayaraj, P., “Message Passing Algorithm: A Tutorial Review”, International Organisation of Scientific Research, vol. 2, pp. 12-24, 2012.