1. A method for decoding low density parity check (LDPC) codes, the method comprising: receiving a priori probability information based on distance vector information relating to distances between received noisy symbol points and symbol points of a signal constellation associated with the LDPC codes; transmitting a posteriori probability information based on the a priori probability information; determining whether parity check equations associated with the LDPC codes are satisfied according to the a priori probability and the a posteriori probability information; selectively regenerating the signal constellation bit metrics based on the determining step; and outputting decoded messages based on the regenerated signal constellation bit metrics.