A receiver of a communication system includes: an input module, a group-based pre-decoding module and a reconstructing module. The input module is for receiving a received data. The group-based pre-decoding module is for combining the received data with a grouped decoding matrix into an encoded equation matrix (EEM) based on a group parameter and for performing a group operation on the EEM. The reconstructing module is for reconstructing the EEM obtained from the group operation into an output data.