Importance sampling for tanner trees

This correspondence presents an importance sampling (IS) simulation scheme for the soft iterative decoding on loop-free multiple-layer trees. It is shown that this scheme is asymptotically efficient in that, for an arbitrary tree and a given estimation precision, the required number of samples is inversely proportional to the noise standard deviation. This work has its application in the simulation of low-density parity-check (LDPC) codes.