A method for error correction and a decoder using low density parity check (LDPC) codes includes initializing extrinsic probability information between variable nodes and check nodes in a bipartite graph including generating a Bernoulli sequence according to a probability of a bit having a value one. Parity checking is performed in accordance with a parity check equation. If the parity check equation is not satisfied, then extrinsic information is updated in check nodes from variable nodes using a parity node update logic circuit in a first half iteration, extrinsic information is updated in variable nodes from check nodes using a variable node update logic circuit in a second half iteration, and the variable nodes are updated with a probability based upon the extrinsic information passed between check nodes and variable nodes wherein the probability represents a likelihood that an ith bit is a one. Information bits are passed when the parity check equation is satisfied or a predetermined number of iterations has been reached.