The alternating direction method of multipliers (ADMM) algorithm for decoding low-density parity-check (LDPC) codes has attracted significant attention because of its superior performance. The convergence characteristic has been regarded as a crucial element to enhance its advantage in practice. In this paper, an efficient ADMM decoder for binary LDPC codes is proposed by adjusting the position of the Euclidean projection to enhance the convergence behavior. The simulation results show that the proposed algorithm can improve the FER performance by 1.1dB as well as save average decoding iterations by 13% compared with the existing CSA when the maximum number of iterations is set to 20. The proposed algorithm can be suitable for use at low-iteration regime in high-throughput scenarios.
The alternating direction method of multipliers (ADMM) algorithm for decoding low-density parity-check (LDPC) codes has attracted significant attention because of its superior performance. The convergence characteristic has been regarded as a crucial element to enhance its advantage in practice. In this paper, an efficient ADMM decoder for binary LDPC codes is proposed by adjusting the position of the Euclidean projection to enhance the convergence behavior. The simulation results show that the proposed algorithm can improve the FER performance by 1.1dB as well as save average decoding iterations by 13% compared with the existing CSA when the maximum number of iterations is set to 20. The proposed algorithm can be suitable for use at low-iteration regime in high-throughput scenarios.
The alternating direction method of multipliers (ADMM) approach to decoding low-density parity-check (LDPC) codes has garnered lots of attention due to its superior error correction performance in error floor regions. However, improving convergence characteristic of ADMM decoding efficiently remains to be a crucial but challenging issue for practical application. In order to tackle this challenge, in this paper we first propose an efficient Pro-ADMM-based decoding algorithm framework by inserting additional quadratic proximal terms to each iteration of ADMM decoding for stabilizing the variable updates. Second, an message-passing interpretation of Pro-ADMM decoder is considered, and then an improved version based on horizontal layered scheduling, named Pro-ADMM-HL decoder is developed to further enhance the convergence behavior of Pro-ADMM decoding. Additionally, we analyze that the complexity of the proposed Pro-ADMM-HL decoders at each iteration displays linearly to LDPC code length. Finally, the effectiveness of the proposed Pro-ADMM and Pro-ADMM-HL decoding algorithm in terms of error correction performance and convergence characteristic is demonstrated by simulation results.
Iterative decoding algorithms based on the alternating direction method of multipliers (ADMM) decoding of low density parity check (LDPC) codes has emerged as an alternating decoding method and bringed a boom of research on drawing upon mathematical optimization to LDPC decoding. Improving error-correcting performance is a key issue to enhance the superiority of ADMM decoding. In this letter, we investigate an efficient ADMM-based iterative decoder for binary LDPC codes. First, we build an mathematical programming equivalence of the maximum likelihood (ML) decoding problem by transforming parity-check constraints to multiple equivalent linear constraints and eliminating check-polytope projection (CPP). Then, an iterative algorithm based on ADMM technique is developed to solve this free-of-CPP (FCPP) equivalence and each ADMM update can be computed efficiently. Moreover, the proposed ADMM-FCPP decoding algorithm is analyzed to display a linear complexity to the length of the LDPC code at each iteration. Finally, simulation results demonstrate the superiority of the proposed decoder in error-correcting performance compared with the state-of-the-art ADMM-based decoders.
This paper presents an efficient quadratic programming (QP) decoder via the alternating direction method of multipliers (ADMM) technique, called QP-ADMM, for binary low-density parity-check (LDPC) codes. Its main contents are as follows: first, we relax the maximum likelihood (ML) decoding problem to a non-convex quadratic program. Then, we develop an ADMM solving algorithm for the formulated non-convex QP decoding model. In the proposed QP-ADMM decoder, complex Euclidean projections onto the check polytope are eliminated and variables in each updated step can be solved analytically in parallel. Moreover, it is proved that the proposed ADMM algorithm converges to a stationary point of the non-convex QP problem under the assumption of sequence convergence. We also verify that the proposed decoder satisfies the favorable property of the all-zeros assumption. Furthermore, by exploiting the inside structures of the QP model, the complexity of the proposed algorithm in each iteration is shown to be linear in terms of LDPC code length. Simulation results demonstrate the effectiveness of the proposed QP-ADMM decoder.
The Alternating Direction Method of Multipliers (ADMM) has proven to be an efficient approach for implementing linear programming (LP) decoding of low-density parity-check (LDPC) codes. By introducing penalty terms into the LP decoding model's objective function, ADMM-based variable node penalized decoding effectively mitigates non-integral solutions, thereby improving frame error rate (FER) performance, especially in the low signal-to-noise ratio (SNR) region. In this paper, we leverage the ADMM framework to derive explicit iterative steps for solving the LP decoding problem for LDPC codes with penalty functions. To further enhance decoding efficiency and accuracy, We propose an LDPC code decoding algorithm based on the symmetric ADMM (S-ADMM). We also establish some contraction properties satisfied by the iterative sequence of the algorithm. Through simulation experiments, we evaluate the proposed S-ADMM decoder using three standard LDPC codes and three representative fifth-generation (5G) codes. The results show that the S-ADMM decoder consistently outperforms conventional ADMM penalized decoders, offering significant improvements in decoding performance.
Mathematical programming (MP) decoding based on the alternate direction method of multipliers (ADMM) algorithm is a promising approach for low-density parity-check (LDPC) codes in recent years. For this kind of decoding, the convergence characteristic has been considered as a key factor to enhance its advantage in practice. In this letter, we propose an efficient decoding algorithm based on generalized Bregman ADMM (G-BADMM) technique to improve the convergence speed of ADMM-based MP decoding for binary LDPC codes. The G-BADMM algorithm is established by adding additional Bregman divergences to the ADMM iterations of MP decoding. Moreover, the resulted G-BADMM iterations are solved efficiently. Furthermore, we theoretically analyze the proposed G-BADMM algorithm including its decoding performance analysis and computational complexity. Simulations demonstrate the efficiency of the proposed G-BADMM-based decoding algorithm.
Alternating Direction Method of Multipliers (ADM-M) is an effective method for Linear Programming (LP) decoding of Low-Density Parity-Check (LDPC) codes. In the ADMM-based LDPC decoding algorithm, Euclidean projection on the check polytope is the key step. Current Euclidean projection algorithms in general require either sorting or iterative operations. However, when decoding LDPC codes with high coding rate, the sorting operation brings a high level of computation complexity. Moreover, although the current iterative projection algorithms do not involve the complex operation of sorting, its convergence speed is slow. In this paper, based on trend extrapolation, a reduced-complexity iterative check polytope projection algorithm is proposed. In the proposed algorithm, the target projection point can be found based on the variation trend of the geometric position of the projection points obtained from previous iterations. Therefore, it ensures fast convergence and does not sacrifice on bit error rate (BER) performance. The simulation results confirm that the proposed algorithm can effectively reduce the decoding complexity, especially for LDPC codes with high coding rate.