Quadratic Programming Decoder for Binary LDPC Codes via ADMM Technique with Linear Complexity

In this paper, we develop an efficient quadratic programming (QP) decoding algorithm via the alternating direction method of multipliers (ADMM) technique for binary low density parity check (LDPC) codes. Its main content is as follows: first, through transforming the three-variables parity check equation to its equivalent expression, we relax the maximum likelihood decoding problem to a quadratic program. Second, the ADMM technique is exploited to design the solving algorithm of the resulting QP decoding model. Compared with the existing ADMM-based mathematical programming (MP) decoding algorithms, our proposed algorithm eliminates complex Euclidean projection onto the check polytope. Third, we prove that the proposed algorithm satisfies the favorable property of all-zeros assumption. Moreover, by exploiting the inside structure of the QP model, we show that the decoding complexity of our proposed algorithm in each iteration is linear in terms of LDPC code length. Simulation results demonstrate that the proposed QP decoder attains better error-correction performance than the sum-product BP decoder and costs the least amount of decoding time amongst the state-of-the-art ADMM-based MP decoding algorithms.