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Journal of Zhejiang University of Technology

The research on quantization issues of quasi-cycle low-density parity check codes based on BP algorithm

XU Zhi-jian

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

The quantization issues of the belief propagation(BP)algorithm for the quasi-cycle low-density parity code(QC-LDPC)of 802.16estandard are studied in this paper.We consider the quantization problem of input signal and mid-variables from the following three aspects:the variables range,bits and methods of the quantization and make a performance simulation and contrast..Then,a innovative and efficient scheme of quantization is proposed in this paper.The quasi-cycle low-density parity code(QC-LDPC)is used here.It has a better performance and it is beneficial for implementation of hardware.Assuming the input is equiprobable signal and the maximum number of iteration is 10,comparing to the standard(non-quantization)BP algorithm,the proposed scheme keeps the lower bit error rate(BER)by means of the MATLAB simulation meanwhile the hardware complexity is greatly reduced.

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The quantization issues of the belief propagation(BP)algorithm for the quasi-cycle low-density parity code(QC-LDPC)of 802.16estandard are studied in this paper.We consider the quantization problem of input signal and mid-variables from the following three aspects:the variables range,bits and methods of the quantization and make a performance simulation and contrast..Then,a innovative and efficient scheme of quantization is proposed in this paper.The quasi-cycle low-density parity code(QC-LDPC)is used here.It has a better performance and it is beneficial for implementation of hardware.Assuming the input is equiprobable signal and the maximum number of iteration is 10,comparing to the standard(non-quantization)BP algorithm,the proposed scheme keeps the lower bit error rate(BER)by means of the MATLAB simulation meanwhile the hardware complexity is greatly reduced.
The quantization scheme for the iterative belief propagation (BP) algorithm of low density parity check (LDPC) codes is studied.The effects of the bound,resolution,and other parameters for uniform and nonuniform quantization schemes are discussed.Good performance of decoding under properly designed quantization can be obtained as shown by simulations.Furthermore,we found that the quantization of high order for the mid variables of BP decoding algorithm can improve the performance and reduce the error floor of LDPC codes at regions of high signal to noise ratio.
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 proposes a two-stage iterative decoding scheme named matrix transform belief propagation scheme (MT-BP) based on conventional belief propagation (BP) algorithm for lowdensity parity-check (LDPC) codes.By introducing information measurement, location vectors and parity check matrix transform, the proposed method can establish additional parity check equations and take more information bits of variable nodes into consideration compared with conventional BP algorithm.The simulations are performed on random regular LDPC codes and algebraic quasi-cyclic codes (QC-LDPC), the experimental results show MT-BP method can efficiently reduce the bit error rate (BER).
A novel belief propagation(BP) decoding algorithm for convolutional low-density parity-check codes is proposed.The proposed algorithm raises the efficiency of updating the variable information by applying feedback information at each decoding iteration and employs the weighting factor to reduce the error propagation caused by the cycles in the Tanner graph,thus yielding a faster convergence of the decoding.Simulation results show that an error performance better than that of the existing belief propagation algorithm can be achieved,while the 5/8 decoding delay and the computation complexity are effectively reduced.Compared with the existing BP,the proposed algorithm achieves a gain of 0.16dB at the BER of 10-6 with the same number of iterations.
A low-density parity check (LDPC) code with the belief propagation (BP) or the log-likelihood ratio belief propagation (LLR-BP) can achieve good bit error rate (BER) performance approaching the Shannon limit. When a parity check matrix of the LDPC code has the cycle, the BP and LLR-BP decoding algorithms achieve approximate maximum a posterior probability (MAP) decoding. Although the decoding algorithms are approximate MAP decoding, LDPC codes can achieve very good BER. For the short and middle length LDPC codes, BER and block error rate (BLER) performances are affected by cycle largely. In each iteration, the magnitudes of a posterior LLRs of some bits oscillate owing to cycles. The oscillation is the dominant error factor in the high Eb/Noregion for short and middle length LDPC codes. In this paper, we extend the definition of oscillation to extrinsic LLR (ex-LLR) derived in the bit node process and propose the modified LLR-BP and the modified UMP-BP decoding algorithms. To reduce effects of oscillating ex-LLRs on decoding, for oscillating ex-LLRs, we add the previous ex-LLR to the current ex-LLR. From the computer simulation, we show that for short and middle length LDPC codes, with a simple modification, our proposed decoding algorithms can improve the conventional LLR-BP and UMP-BP decoding algorithms. In particular, we show that the modified UMP-BP decoding algorithm with low complexity can achieve better BER and BLER than the conventional LLR-BP decoding algorithm
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.