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In this letter, we develop an efficient linear programming (LP) decodingalgorithm for low-density parity-check (LDPC) codes. We first relax the maximumlikelihood (ML) decoding problem to a LP problem by using check-nodedecomposition. Then, to solve the resulting LP problem, we propose an efficientiterative algorithm based on the alternating direction method of multipliers(ADMM) technique. In addition, the feasibility analysis of the proposedalgorithm is presented. Furthermore, through exploiting the sparsity andorthogonality structures of the LP problem, the computational complexity of theproposed decoding algorithm increases linearly with the length of the LDPCcode. Simulation results demonstrate that our proposed algorithm achievesbetter performance than other competing algorithms in terms of decoding time.

Minimum-Polytope-Based Linear Programming Decoder for LDPC Codes via ADMM Approach