Binary LDPC Codes Decoding Algorithm Based on MRF and FPGA Implementation

Abstract

IntroductionLDPC code, low density parity check code [1][2][3], belongs to the linear block code. Its check matrix is sparse matrix of 0 and 1. Generalized LDPC codes have shown relatively good performance. Scholars Gallage brought forward the related theory basis of LDPC codes in 1962 [4]. Because the LDPC code decoding complexity is not high, and its description is relatively simple, it can be realized by hardware, so it immediately draw attention and became academic research hot [5]: increasing the transmission distance, proposing energy-saving scheme and improving anti interference ability, etc [6]. In fact, the research steps of further enhancing the performance of LDPC codes never stop. LDPC codes have been extensively studied in the literature using code modifying techniques such as information nulling or shortening, extending [7,8], puncturing [9], and combining [10]. We focused on studying the structure of LDPC code and LDPC code decoding algorithm, improved LDPC code decoding algorithm became the most crucial part [11].Due to the progress of computer computing capacity, the calculation of stochastic model is no longer the bottleneck, we give more and more attention to stochastic model, and Markov [12] Random Field is one of the important branches. MRF introduced structure information through the neighborhood system, so that it can express interaction model between spatial relative random variables, and find the solution of the problem according to the statistical decision and estimation theory optimal criterion. No matter hard decision or soft decision LDPC code decoding algorithm, after optimizing ring detection algorithm, we put forward the application of Gaussian Markov Random Field model to realize the source parameter estimation, and realize the LDPC code decoding algorithm based on MRF.The best way of testing whether an algorithm is effective is to apply the algorithm to practice it. So we use FPGA [13] model to realize the algorithm, and to verify the effectiveness, so that it can provide guidance when we use this algorithm in bad communication environment.

Research and Implementation of High-Efficiency and Low-Complexity LDPC Coding Algorithm

“…The iterative message of the BP algorithm is generally expressed in the form of probability or LLR. The advantage of the LLR-BP algorithm over the probabilitybased BP algorithm lies in transforming many multiplication operations into additive operations, thus considerably relieving the implementation complexity of decoding while preserving the decoding performance [5,[18][19][20][21][22][23][24][25][26][27][28][29].…”

“…The MSA algorithm, a simplified form of the LLR-BP algorithm, performs the following simplification during the check nodes update [22][23][24][25][26][27][28][29][30][31][32]:…”