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International Conference on Mechatronics Engineering and Information Technology (ICMEIT)

Research and Improvement of LPDC Decoding Algorithm

Tingting Chen, Riuan Liu, Lirong Diao

Published Jan 1, 2016• 0 citations
Publisher

Abstract

Low Density Parity Check(LDPC) code itself has a good performance and the application of LDPC in the communication field is extensive.LDPC codes have the characteristics of low bit error rate, easy adjustment, low decoding complexity and excellent decoding performance.LDPC is considered to be the "best performance" in the field of coding and decoding [1] .In this paper, we mainly introduce the theory of LDPC codes.And the use of the method of the LDPC code to do a further explanation.Several simple decoding schemes of LDPC are studied.Finally, using the method of function approximation to replace the confidence function to improve the BP LLR algorithm, and simulation experiments are carried out.

DOI
10.2991/icmeit-16.2016.14

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Low Density Parity Check(LDPC) code itself has a good performance and the application of LDPC in the communication field is extensive.LDPC codes have the characteristics of low bit error rate, easy adjustment, low decoding complexity and excellent decoding performance.LDPC is considered to be the "best performance" in the field of coding and decoding [1] .In this paper, we mainly introduce the theory of LDPC codes.And the use of the method of the LDPC code to do a further explanation.Several simple decoding schemes of LDPC are studied.Finally, using the method of function approximation to replace the confidence function to improve the BP LLR algorithm, and simulation experiments are carried out.
Low density parity check code is a kind of high-performance linear block code. It has excellent performance which is near the Shannon limit. LDPC has low decoding complexity, free structure and receives extensive attention. The typical decoding algorithm of LDPC is LLR BP algorithm, which is also called “sum-product algorithm”. LLR BP algorithm is the best algorithm at present. But it needs complex computation, which causes great difficulty in its hardware design. To solve this problem, an algorithm that gets approximation of LLR BP algorithm is put forward, which is called min-sum algorithm. Min-sum algorithm greatly reduces the computation and makes the hardware design simpler, but its accuracy has a wide gap with BP algorithm. This article analyzes the reason why min-sum algorithm has errors, and puts forward an improved algorithm called min-sum linear approximation algorithm based on min-sum algorithm.
Low density parity check (LDPC) code is a kind of linear block code with excellent performance which is proposed by Dr. Gallager. It overcomes the shortcomings of other error correcting codes and it is the nearest channel code from Shannon limit at the present discover. The decoding algorithms of L DPC code can reduce the decoding delay by the parallel decoding structure, so this has caused great concern in many fields. In recent years more and more scholars begin to study LDPC code, this makes the coding and decoding algorithms of LDPC code improved continuously. LDPC code has been widely used in many fields such as optical fiber communication, digital watermarking, underwater communication and deep space communication because of its excellent performance. Non-binary LDPC code has better performance compared with binary LDPC code. In this paper, FFT-BP decoding algorithm of non-binary LDPC code is studied, and on this basis, we proposed an improved FFT-BP algorithm. The improved decoding algorithm can effectively reduce the average iteration number. Finally, we achieved encode and decode algorithm of non-binary LDPC code with FPGA.
Reduced-Complexity Decoding of LDPC Codes Various log-likelihood-ratio-based belief-propagation (LLR- BP) decoding algorithms and their reduced-complexity derivatives for low-density parity-check (LDPC) codes are presented. Numerically accurate representations of the check-node update computation used in LLR-BP decoding are described. Furthermore, approximate representation of the decoding computations are shown to achieve a reduction in complexity, by simplifying the check-node update or symbol-node update, or both. In particular, two main approaches for simplified check-node updates are presented that are based on the so-called min-sum approximation coupled with either a normalization term or an additive offset term. Density evolution is used to analyze the performance of these decoding algorithms, to determine the optimum values of the key parameters, and to evaluate finite quantization effects. Simulation results show that these reduced-complexity decoding algorithms for LDPC codes achieve a performance very close to that of the BP algorithm. The unified treatment of decoding techniques for LDPC codes presented here provides flexibility in selecting the appropriate scheme from a performance, latency, computational complexity, and memory-requirement perspective.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.
LDPC (Low Density Parity Check Codes) is a low -density puppet test code applied to channel codes. Among the existing LDPC decoding algorithms, the LLR-BP decoding arithmetic is too complicated to calculate the calculation due to the containing a large number of bilateral positive cut functions. Therefore, this article proposes a LDPC decoding algorithm that combines the Modified Weighted Bit Flipping Decoding Algorithm (MWBF) with the Logarithmic Likelihood Ratio Based Confidence Propagation Algorithm (LLR-BP). In the process of the LLR-BP decoding iteration, the introduction of the MWBF algorithm not only does it reduce the complexity of iteration and decoding, but also avoids the traditional weighted bit-flipping decoding algorithm (WBF). Excessive effects of code performance.
Low-density parity-check code (LDPC) not only has good performance approaching the Shannon limit, but also has low decoding complexity and flexible structure. It is a research hot-spot in the field of channel coding in recent years and has a wide range of application prospects in optical communication systems. In this paper, the decoding aspects and performance of LDPC codes are analyzed and compared according to the bit error rate (BER) of LDPC codes. The computer simulation was carried out under additive white Gaussian noise (AWGN) channel and binary phase shift keying (BPSK) modulation. Through theoretical analysis and simulation results, this paper explores the way of multi-rate LDPC decoding.