Mathematical analysis of an iterative algorithm for low-density code decoding

Zheng He, Huaying Zhou, Hanying Hu

In this paper, we propose an improved graph-based Chase-MP algorithm for iterative decoding of generalized low-density (GLD) codes, and also present analysis of the iterative decoding by using the Gaussian approximation. The simulation results on the additive white Gaussian noise (AWGN) channel show that the proposed algorithm can achieve good performance. During the iterative decoding analysis, we get a dynamic mathematical model of the Gaussian mean on iterations. As an application of the model derived, we compute decoding thresholds for several extended Bose-Chaudhuri-Hocquengnem (eBCH)-component GLD codes

Junho Cho

Tadashi Wadayama

Jing Bai, Yuhao Chi, Chau Yuen

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.

Martin Bossert, F. Hergert

Dmitri V. Truhachev, Michael Lentmaier, Kamil Sh. Zigangirov

Asymptotic iterative decoding performance of low-density parity-check (LDPC) convolutional codes is analyzed. An important role within the analysis is a theorem on the minimal length of cycles in the Tanner graph describing a code.