1. A receiving system adapted to receive through a channel at least N modulated data that are encoded through parity-check (PC) coding, the receiving system comprising: a channel estimator to estimate a channel quality ratio of a channel receiving quality based on the modulated data; and a PC code decoder, coupled to said channel estimator, to obtain at least N bit nodes based on the modulated data, said PC code decoder including a verifying circuit, a reliability-generating circuit, a bit-exchange circuit, a check-exchange circuit, and a reliability-updating circuit.