A decoding algorithm with an enhanced parity check matrix and a re-encoding scheme for LDPC codes is disclosed. The decoding algorithm includes the steps of: providing the enhanced parity check matrix; receiving a message part of an original codeword encoded by a generator matrix from the enhanced parity check matrix; setting a LLR for each bit node of the enhanced parity check matrix; processing hard decision on the message part of the original codeword; encoding the message part of the original codeword by the generator matrix to generate a new codeword having a generated parity part; comparing the original parity part with the generated parity part to find out bits of difference; voting candidate error bits to choose the most probably erratic bits; modifying LLR of the chosen bits to have a modified codeword; and processing a conventional iterative decoding procedure on the modified codeword to have a processed codeword.