Improved Gradient Descent Bit Flipping Algorithms for LDPC decoding Tharathorn Phromsa-ard, Jiratchaporn Arpornsiripat, Jutaphet Wetcharungsri, Paramin Sangwongngam and Keattisak Sripimanwat. Optical and Quantum Communications Laboratory (OQC). National Electronics and Computer Technology Center (NECTEC), NSTDA. Pathumthani, Thailand. E-mail: tharathorn.phromsaard@gmail.com Pisit Vanichchanunt Department of Electrical and Computer Engineering. Faculty of Engineering. King Mongkut's University of Technology North Bangkok (KMUTNB). Bangkok, Thailand. Abstract—For LDPC decoding, a class of weighted bit-flipping algorithms is much simpler than a belief propagation algorithm. This work proposes a modified Gradient Descent Bit-Flipping algorithm based on Reliability Ratio with an adaptive threshold to address trade-off between performance and latency. From numerical results, the proposed algorithm achieves lower latency without an expense of performance. It yields average iteration reduction of 15–27% over SNR range from 2.5 dB to 4.5 dB. In addition, it provides better decoding performance gains, i.e. 0.05– 0.25 dB over low-to-medium SNR range between 1.5 dB and 4 dB comparing to previous schemes. Keywords-component; LDPC Codes, bit flipping algorithms, decoding, latency. I. INTRODUCTION Low-density parity-check (LDPC) [1] [2] codes receive much attention to research community and industrial sectors. They are adopted to numerous implementation and standards in various applications, such as hard disk drives, WLAN, WiMAX and satellite DVB. LDPC codes can be decoded using several decoding schemes: soft-decision, hard-decision [1], and hybrid decoding [3–14]. A soft decoding scheme called message passing algorithm (MPA) or belief propagation algorithm (BPA) was shown to be near channel capacity. However, this algorithm characterizes very high computational complexity. Bit flipping algorithms (BFA) [1] is a hard decision scheme which possesses a good trade-off between error-correcting performance and decoding complexity compared to BPA and its variants such as sum-product and min-sum algorithms. Therefore, a hybrid scheme of soft and hard decision called Weighted Bit-flipping (WBF) [3] is created to fulfill practical requirements on complexity in hardware. There are many variants of WBF algorithm. They are invented to address three important problems: BER performance (coding gain), computational complexity and latency issues. The issues can be found as trade-off problem where a challenge is to optimize all of them under specific requirements. While WBF algorithm only considers the information provided by the check node, the modified WBF (MWBF) algorithm [4] considers the information supplied by both the check nodes and the message nodes with the optimal weighting factor α . Then, an improved MWBF (IMWBF) algorithm [5] was proposed to compute reliability of the parity checks and approximate analysis of the optimal weighting factor. It exhibited BER performance improvement in expense of computational complexity. The reliability ratio WBF (RRWBF) [6] [7] algorithm normalizes a value of the received soft values resulting in improved error correcting performance. A new way of schemes is optimization approach to BFA, which is a decision metric based on the gradient descent formulation. Gradient Descent Bit-Flipping (GDBF) [11] algorithm outperformed the WBF and MWBF algorithms in error correcting ability and more significantly in an average number of iterations. Then, adaptive threshold techniques have been applied for both the BFA [12] and gradient descent (GD) algorithm [13][14]. It was shown to provide low latency and low power [13], but performance degradation when compared with a multi-GDBF. In this paper, a modified reliability ratio GDBF algorithm and an adaptive threshold depending on the mean of the negative inversion and variance of received signals are presented in order to gain better performance and reduce a number of iterations. The paper is organized as follows. The system model for problem formulation and review bit-flipping algorithms are discussed in Section II. A proposed Reliability Ratio based Weighted Gradient Descent Bit Flipping (RRWGDBF) methods are described in Section III. The numerical results are presented and discussed in Section IV and finally conclusions are drawn in Section V. II. PRELIMINARIES A. Notation LDPC codes are a class of linear block codes defined by their sparse parity check matrices n m ij h × = ) ( H of size n m ×