Locally-Optimized Reweighted Belief Propagation for Decoding LDPC Codes with Finite-Length

In practice, LDPC codes are decoded using message passing methods. These methods offer good performance but tend to converge slowly and sometimes fail to converge and to decode the desired codewords correctly. Recently, tree-reweighted message passing methods have been modified to improve the convergence speed at little or no additional complexity cost. This paper extends this line of work and proposes a new class of locally optimized reweighting strategies, which are suitable for both regular and irregular LDPC codes. The proposed decoding algorithm first splits the factor graph into subgraphs and subsequently performs a local optimization of reweighting parameters. Simulations show that the proposed decoding algorithm significantly outperforms the standard message passing and existing reweighting techniques.