LDPC codes have many applications in channel and source coding. In this thesis, we apply LDPC-like belief propagation algorithm to address distributed detection problem in Wireless Sensor Network. The objective is to achieve convergence to a weighted average and to make decision at all sensor nodes. We also consider the design of WSN structure, which achieves convergence asymptotically, and guarantees the consensus of all sensor nodes. We study the network structures that can achieve the fastest convergence. The results show analogy to the performance of LDPC codes in channel coding. Introducing certain range of irregularity results in an improvement in the network performance in terms of the rate of convergence.