Iterative Decoding using Eigenmessages

The eigenmessage approach to iterative decoding introduces a degree of nonlocality into a belief propagation decoder by representing an entire set of messages around a cycle of the Tanner graph as a linear operator. The eigenvector for the operator represents a fixed point of the belief propagation algorithm around a cycle, with incident messages fixed. A multiple eigenmessage approach is also presented, in which messages around several cycles are simultaneously expressed. The eigenmessage approach may be applied to any graph with cycles, but we demonstrate its use on LDPC decoding. In this setting, computational results compare eigenmessage methods with conventional belief propagation decoding showing, using simulation and EXIT charts, that the eigenmessage approaches slightly reduce the number of decoder iterations compared to belief propagation decoding while preserving the probability of error of conventional decoding.