A parity-check-code decoder is adapted for receiving a channel quality ratio and at least (N) bits that are to be decoded. The parity-check-code decoder treats each of the bits as a bit node, and includes: a verifying circuit that multiplies (N) bit nodes by a matrix to obtain (N-K) check nodes; a reliability-generating circuit that generates a reliability index that serves as an extrinsic check index for each of the bit nodes to transmit to the check nodes; a bit exchange circuit that generates an extrinsic bit index for each of the check nodes to transmit to the bit nodes; a check-exchange circuit that updates a plurality of the extrinsic check indices based on the extrinsic bit indices for the bit nodes to transmit to the check nodes; and a reliability-updating circuit that updates the reliability index of and determines an updated value for each of the bit nodes.