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The Euclidean projection onto check polytopes is the most time-consuming operation in the linear programming (LP) decoding based on alternating direction method of multipliers (ADMM) for low-density parity-check (LDPC) codes. In this letter, instead of reducing the complexity of Euclidean projection itself, we propose a new method to reduce the decoding complexity of ADMM-based LP decoder by decreasing the number of Euclidean projections. In particular, if all absolute values of the element-wise differences between the input vector of Euclidean projection in the current iteration and that in the previous iteration are less than a predefined value, then the Euclidean projection at the current iteration will be no longer performed. Simulation results show that the proposed decoder can still save roughly 20% decoding time even if both the over-relaxation and early termination techniques are used.Index Terms-Linear programming decoding, alternating direction method of multipliers (ADMM), reduce-complexity.

Based on linear programming (LP) decoding with alternating direction method of multipliers (ADMM), Liu et al. proposed an ADMM penalized decoder for low-density parity-check (LDPC) codes that can improve the error rate performance at low signal-to-noise ratios. In this letter, we propose a new ADMM penalized decoder to improve the error rate performance further for irregular LDPC codes. The proposed decoder modifies the penalty term of the objective function by assigning different penalty parameters for different variable node degrees. Simulations over three irregular LDPC codes show that the proposed decoder performs considerably better than the ADMM penalized decoder.Index Terms-Alternating direction method of multipliers (ADMM), linear programming (LP) decoding, penalized ADMM decoder.

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