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