The performance of a linear code under iterative decoding over the binary erasure channel is determined by stopping sets. The relationship between stopping sets in a few parity-check matrices of a given product code and those in the parity-check matrices for the component codes is determined. We derive upper bounds on the stopping redundancy of product codes based on the stopping redundancy of the component codes, and then obtain new upper bounds on the stopping redundancy of product codes and show how they improve the before known results. It is shown that the multidimensional single parity-check product codes are the optimal stopping redundancy codes. In this thesis, construction of high stopping-distance low-density parity-check product codes with finite geometry LDPC and Hamming codes as the constituent codes is considered. It is shown that these codes have high stopping distance compared to the other LDPC codes. For example, linear [511, 180, 30], [945, 407, 27], [2263, 1170, 30] and [4095, 2101, 54] LDPC codes are designed with the stopping distances 30, 27, 30 and 54, respectively. It is well known that the decoding failure probability of iterative decoding over the BEC is computed by the multiplicity of the stopping distance when the erasure probability is small. The decoding failure probability of iterative decoding for Hamming product codes are studied. It is shown that the decoding failure probability of iterative decoding for Hamming product code is near the decoding failure probability of the maximum likelihood and row-column decoding when the erasure probability is small. Key Words: Stopping distance; Stopping redundancy; LDPC codes; product code.