The present invention provides a low-complexity and multi-mode Low-density Parity-check (LDPC) codec, in which the decoding operations are divided into small tasks and a unified hardware is implemented so that the hardware resources can be reused in different modes. In addition, memory access is achieved via routing networks with fixed interconnections and memory address generators, the complexity of the hardware implementation is reduced accordingly. Further, the present invention provides an early termination function with which the iterative operations can be terminated early when a threshold is reached so that the power consumption can be thus reduced. The hardware resources for early termination shares a part of hardware resources with an encoder according to the present invention so that the complexity of the hardware implementation can also be reduced.