Efficient MP Decoding via Fast G-BADMM Approach for Binary LDPC Codes

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.