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Electronic Science and Technology

Research into Non-binary LDPC Decoding Performance Factors

Ming Diao

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

The non-binary LDPC is the promotion to the finite GF(q) of binary LDPC codes.The parity check matrix elements is no longer 0 and 1,but collections(0,1,2,…,q-1),while the decoding still uses the efficient iterative decoding based on belief propagation algorithm.This paper focuses on the check matrix of structure of the quasi-cyclic LDPC codes(QC-LDPC) as well as the min-sum decoding algorithm.Then the LDPC codes decoding performance is simulated under different conditions in white Gaussian noise channel(AWGN) with Matlab.Finally,the impact of non-binary LDPC Decoding performance factors is analyzed.

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The non-binary LDPC is the promotion to the finite GF(q) of binary LDPC codes.The parity check matrix elements is no longer 0 and 1,but collections(0,1,2,…,q-1),while the decoding still uses the efficient iterative decoding based on belief propagation algorithm.This paper focuses on the check matrix of structure of the quasi-cyclic LDPC codes(QC-LDPC) as well as the min-sum decoding algorithm.Then the LDPC codes decoding performance is simulated under different conditions in white Gaussian noise channel(AWGN) with Matlab.Finally,the impact of non-binary LDPC Decoding performance factors is analyzed.
Non-binary LDPC codes are obtained by generalizing binary LDPC coeds from finite field GF(2) to finite field GF(q).Its elements of parity check matrix are not(0,1),but ensemble(0,1,…,q-1),and its decoding method still employs belief propagation and iterative algorithm.This paper mainly derives the iterative formulas of decoding algorithm for Non-Binary LDPC codes and analyzes an improved algorithm based on FFT.Finally,the predominant performance of FFT decoding algorithm is verified by simulation.
Low-density parity check (LDPC) codes are known to perform well in the presence of additive white Gaussian noise (AWGN) but for very large block lengths. It has been proposed to define the codes over high order Galois fields to overcome this limitation. In this paper we construct new quasi-cyclic non-binary LDPC codes with moderate code lengths from Reed-Solomon codes with two message symbols proposed by Lin et al defined over large finite fields. We evaluate the performance of these codes on the AWGN channel by computer simulation and show that they outperform binary LDPC codes of the same length in binary bits.
Low-density parity-check (LDPC) codes over finite fields GF(q) have a better performance than those of the binary low-density parity-check codes, at short and medium block lengths, but the decoder of GF(q)-LDPC has more complexity. In this paper, we present a new reduced-complexity belief propagation (BP) decoding algorithm for GF(q)-LDPC codes by analyzing the reliability of code symbols. Instead of update all the variable nodes during iteration, we just update variable nodes which are mostly to be in an error. The algorithm also shows a property to reduce the effects of oscillating on decoding. The simulations prove that we could improve performance and reduce complexity at the same time for short and medium GF(q)-LDPC codes.
This paper presents a different decoding techniques for Quasi-Cyclic (QC) Low Density Parity Check (LDPC) code. QC-LDPC code is proposed to reduce the complexity of the Low Density Parity Check code while obtaining the similar performance. The encoding and decoding processes of these codes are easy to simplify and implement. The algorithm used for encoding and decoding are based on matrices and implemented on MATLAB for simulation results. In this paper decoding technique QC-LDPC is introduced and compare the performance of LDPC and QC-LDPC. The decoding techniques is conducted by different algorithms such as Bit Flipping (BF), Belief Propagation (BP) Log, Belief Propagation (BP) Probabilistic (Prob), Belief Propagation (BP) Log Simple.
This paper presents an improved decoding algorithm of non-binary LDPC codes based on the Expanded Min-Sum algorithm,analyzes the complexity of the algorithm in decoding efficiency.According to the fact that the reliability of variable note is increased with the increase of the iterative number,the reliability of the variable notes is estimated by the maximum post probability of variable notes and illegal parity-check values.By the estimation rule,the iterative calculations or some variable notes are stopped,the number of calculation for updating variable and parity-check notes is reduced,thus the decoding complexity is decreased and the decoding efficiency is improved.A simulation is made using regular non-binary LDPC codes under White Gaussian Noise channel based on GF(4),the result shows that the performance decreases by about 0.05 dB when BER(Bit Error Rate) is,but the decoding complexity is reduced and the decoding efficiency is improved significantly.
Quasi Cyclic Low Density Parity Check(QC-LDPC) code is an important branch of LDPC code research.It is a kind of constructed LDPC code with check matrix H constructed by quasi cyclic method.IEEE 802.16e proposes a parity check matrix with quasi cyclic character which makes the encoding and hardware easy to be implemented.This article will mainly introduce the encoding process and analyze the decoding performance of various decoding algorithms.Simulations show that Min-Sum(MS) algorithm compares to the Log-BP performance has approximately 0.5dB loss for high-speed rate coding.And the performance of Normalized Min-Sum(NMS) and Row Weight Matched Min-Sum(Rwm-MS) with relatively low complexity is nearly the same as that of Log-BP algorithm.