Two iterative decoding methods, message passing algorithm (MPA) and linear programming (LP) decoding, are studied and explained for an arbitrary LDPC and binary linear block codes. The MPA, sum-product and maxproduct/ min-sum algorithm, perform local decoding operations to compute the marginal function from the global code constraint defined by the parity check matrix of the code. These local operations are studied and the algorithm is exemplified. The LP decoding is based on a LP relaxation. An alternative formulation of the LP decoding problem is explained and proved. An improved LP decoding method with better error correcting performance is studied and exemplified. The performance of two methods are also compared under the BEC.

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