This was a course project for CS6782 – Probabilistic graphical models. In this project, I study the application of two techniques to the belief-propagation based decoding of LDPC codes, and compare these techniques against a traditional sum-product LDPC decoder. The first technique, min-sum decoding was implemented in the 1980s by Tanner as a method to reduce computational complexity of sum-product decoding. The other technique, residual belief propagation optimises the order in which message updates are scheduled in an informed manner, leading to faster and better convergence. The two methods are combined and experimentally evaluated.