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This paper investigates the connection between the classical sum-product (SP) decoder for low density parity check (LDPC) codes and the recently proposed gradient projection (GP) decoding scheme presented in (Kasparis and Evans, 2007). A graphical model for GP is exhibited based on which we derive an intermediate algorithm which establishes a bridge between graphical based algorithms (SP and variants) and an optimization based algorithm (GP). A more practical decoding algorithm with improved performance and reduced complexity is also proposed. A complexity analysis is provided and performance are studied through Monte-Carlo simulations.