Abstract: The alternating direction method of multipliers （ADMM） algorithm has emerged as an innovative decoding solution for 5G low-density parity-check （LDPC） codes， leveraging two key features： geometrically-aware processing of linear programming （LP） decoding constraints and efficient implementation of message passing mechanisms. By incorporating a penalty term into the objective function of the LP decoding model， ADMM-based variable node penalty decoding effectively mitigates non-integral decomposition， thereby enhancing frame error rate （FER） performance. Despite the strong performance of ADMM in various practical applications， its relatively slow convergence speed and sensitivity to initial conditions and parameter tuning hinder its effectiveness in high-dimensional and real-time demanding scenarios. In particular， during the LDPC linear programming decoding process， the alternating update mechanism of ADMM can result in oscillation along the optimization path and exhibit suboptimal performance when handling imprecise constraints. To address the issue of slow convergence of the ADMM algorithm， we proposed a new optimization algorithm that integrates Nesterov momentum acceleration with ADMM. This approach aims to mitigate the impact of the ADMM algorithm on the error correction performance and convergence speed of LDPC decoders. By introducing a momentum term， the algorithm reduces the number of iterations and extends Nesterov’s accelerated scheme from unconstrained composite optimization problems to the ADMM penalty function model. First， the ADMM algorithm was employed to effectively reformulate the constraints of the original problem as a component of the objective function， thereby transforming it into an unconstrained optimization subproblem. Building on this foundation， Nesterov acceleration technology was further used to enhance the gradient descent iteration process to improve both convergence speed and solution accuracy. Simulation experiments were conducted using three different rates of 5G LDPC short codes. Compared to existing ADMM-based penalty decoding algorithms， the proposed momentum-accelerated ADMM decoding algorithm achieved a signal-to-noise rate gain of approximately 0.2 dB and reduced the average number of iterations by approximately 20%， thereby accelerating the convergence speed.