Characterization of Factor Graph by Mooij's Sufficient Condition for Convergence of the Sum-Product Algorithm
Recently Mooij et al proposed new sufficient conditions for convergence of the sum product algorithm and it was also shown that if the factor graph is a tree Mooijs sufficient condition for convergence is always activated. In this letter we show that the converse of the above statement is also true under some assumption and that the assumption holds for the sum product decoding. These newly obtained fact implies that Mooijs sufficient condition for convergence of the sum product decoding is activated if and only if the factor graph of the a posteriori probability of the transmitted codeword is a tree
factor graph convergence of the sum product algorithm sum product decoding message passing ldpc codes