This paper has presented various min-sum related LDPC decoding algorithms and their typical hardware architectures of check node update in the scenario of parallel implementation. The m-to-2m decoder has been introduced to generate more efficient new hardware implementations of check node update, which can obviously reduce the number of multiplication operations for normalized min-sum algorithm for high rate LDPC codes. Simulations have claimed the performance of normalized min-sum is nearly the same as that of Log-BP, namely the optimal algorithm. In general, this paper has proved that normalized min-sum is good choices as LDPC decoding methods.