In the Sum Product Algorithm (SPA) for LDPC decoding the messages are sent from the check nodes to bit nodes after the SPA steps which are (for one iteration): initialization of all bit nodes by the Log-likelihood ratios (LLRs) from the channel; for all check nodes and in the bit nodes positions corresponding to 1 in the H matrix, calculation of the variable nodes updates are done based on Log-tanh equation; for each variable node the total update is calculated by the summation of all updates that come from all check nodes which are connected to this variable node; at the end, the new variable nodes values are overwritten by adding the old variable nodes values to their corresponding total updates.
Min Sum Algorithm (MSA) is a simplified version of SPA where the calculation of the variable nodes updates per check equation are done based on finding the minimum value of the variable nodes absolute values and the product of their signs instead of Log-tanh equation.
The design of Flash Memory LDPC decoder is supplied as a portable and synthesizable Verilog IP.