An operating method of an error correction decoder includes receiving data, setting initial log-likelihood values of variable nodes, and decoding the received data by updating a log-likelihood value of a selected variable node by use of a minimum value and a minimum candidate value associated with the selected variable node. The minimum value indicates a minimum value of absolute values of log-likelihood values of first variable nodes sharing a check node with the selected variable node and including the selected variable node. The minimum candidate value indicates one from among absolute values of log-likelihood values of second variable nodes that has the smallest value greater than the minimum value. The second variable nodes are selected later than one from among the first variable nodes corresponding to the minimum value.