Recently, an iterative soft information reliability-based majority-logic (ISRB-MLG) decoding algorithm was proposed for Euclidean geometry LDPC (EG-LDPC) and Projective geometry LDPC (PG-LDPC) codes. This paper first presents an iterative soft information reliability-based min-sum (ISRB-MS) decoding algorithm based on ISRB-MLG and traditional min-sum decoding algorithm. The performance of ISRB-MS algorithm is greatly improved with a little more complexity than ISRB-MLG algorithm, it mainly needs integer additions and logical operations. Different from traditional min-sum decoding algorithm, the extrinsic information transfer of ISRB-MS algorithm is simplified, we use the full information that all check nodes pass rather than the extrinsic information to update the bit nodes information. Then a modified iterative soft information reliability-based min-sum (MISRB-MS) decoding algorithm is proposed. Compared to (ISRB-MS) algorithm, MISRB-MS algorithm multiplies a scaling factor, so it needs some extra multiplication, but it achieves better performance. Simulation results show that the two algorithms achieve excellent performance and fast convergence rate, they only needs about 10 iterations, if an appropriate scaling factor is chosen, the performance of MISRB-MS algorithm very closes to that of sum-product algorithm (SPA).