1. A decoding algorithm with an enhanced parity check matrix and a re-encoding scheme for LDPC codes, comprising the steps of: A. providing the enhanced parity check matrix which is formed by a plurality of sub-matrixes, wherein a first identity matrix in a specific location; B. receiving a message part of an original codeword encoded by a generator matrix from the enhanced parity check matrix with at least one bit is corrupted; C. setting a Log-Likelihood Ratio (LLR) for each bit node of the enhanced parity check matrix while keeping receiving an original parity part of the original codeword; D. processing hard decision on the message part of the original codeword; E. encoding the message part of the original codeword by the generator matrix to generate a new codeword having a generated parity part; F. comparing the original parity part with the generated parity part to find out bits of difference; G. voting candidate error bits to choose the most probably erratic bits; H. modifying LLR of the chosen bits to have a modified codeword; and I. processing a conventional iterative decoding procedure on the modified codeword to have a processed codeword.