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Science Technology and Engineering

Research on an Improved Decoding Algorithm for Low-density Parity-check Codes

Xiyuan Chen

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

To solve the problem of high average running time,an improved decoding algorithm was proposed which was combined by BP algorithm and WBF algorithm.The parity check was added in each BP iterative decoding,and flipping criterions which were passed from check nodes to information nodes were weighted by the reliable information of received sequence.Then a bit flipping measure was to be taken according to specific rules in order to obtain correct codes,and a parity check was added again.Simulation results on Additive White Gaussian Noise(AWGN) channel show that,the improved algorithm can decrease the average running time effectively for LDPC codes while maintaining the excellent decoding performance as BP algorithm.And compared with classical BP algorithm,the effect of the different maximum numbers of iterations,different lengths of codes and different code rates for the improved decoding algorithm are analyzed.

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To solve the problem of high average running time,an improved decoding algorithm was proposed which was combined by BP algorithm and WBF algorithm.The parity check was added in each BP iterative decoding,and flipping criterions which were passed from check nodes to information nodes were weighted by the reliable information of received sequence.Then a bit flipping measure was to be taken according to specific rules in order to obtain correct codes,and a parity check was added again.Simulation results on Additive White Gaussian Noise(AWGN) channel show that,the improved algorithm can decrease the average running time effectively for LDPC codes while maintaining the excellent decoding performance as BP algorithm.And compared with classical BP algorithm,the effect of the different maximum numbers of iterations,different lengths of codes and different code rates for the improved decoding algorithm are analyzed.
Two simple and efficient weighted bit flipping(WBF)decoding algorithms for low density paritycheck(LDPC)codes are proposed,in which the sum of the variable nodes' magnitude is introduced to compute the reliability of the parity checks.Simulation results shows that the performance of one of the improved scheme is better than that of traditional WBF and modified WBF(MWBF)algorithms about 1.65dB and 1.31dB at BER of 10-5 over an additive white Gaussian noise channel,respectively,while the average number of decoding iterations is significantly reduced.
In this paper,several conventional decoding algorithms of LDPC(Low-Density Parity-Check) codes over Additive White Gaussian Noise(AWGN) channels are investigated,and an improved decoding algorithm based on integer operation is proposed. Compared to normalized min-sum algorithm,a modified factor to improve the decoding performance is designed according to the states of hard decision in each iteration. It is convenient for hardware implementation with integer operation.The simulation results show that the algorithm performs better than LLR BP decoding algorithm in 2.1 dB and decodes fast with low complexity.
In this paper, a new method for improving hard-decision bit-flipping (BF) decoding is proposed for low-density parity-check codes. The flipping criterion is derived theoretically from the soft-decision belief-propagation decoding algorithm. The proposed BF decoding algorithm is channel independent and is improved by introducing a more efficient method for computing the reliability of the parity checks. Extensive simulations are provided to demonstrate the efficiency of the proposed algorithm. Simulation results show that the proposed algorithm can achieve about 1.5dB coding gain improvement at BER = 5×10−6while reducing up to 48% iterations for decoding and maintaining low decoding complexity, compared with the conventional weighted BF algorithm.
An improved belief propagation(BP) decoding scheme was put forward to solve the high complexity and low decoding efficiency problem of BP in low density parity check(LDPC) codes.Because different bit nodes and check nodes have different reliability and contribute differently to BP decoding;the proposed decoding scheme employs a differentiate rule based on lawless check number and pseudo posterior probability to evaluate every bit's reliability before each step of iteration;The nodes have little lawless check number and large pseudo posterior probability are supposed to have higher reliability.The bits with high reliability need not to be updated by the decoder.Simulation shows that the proposed BP decoding algorithm can reduce the computational load and increase the decoding efficiency significantly.
To further improve the decoding performance of the Normalized BP-Based algorithm,an improved Normalized BP-Based algorithm was proposed.The correction factor was changed dynamically according the amount of the information from the check nodes to variable nodes in order to achieve non-linear compensation of BP-Based algorithm.The simulation results show that when the bit error rate was less than 0.5×10-2,the improved algorithms could get about 0.1 dB gain,compared with Normalized BP-Based algorithm,only with slight increase in complexity,and the number of iterations did not increase.
In order to reduce the bit error rate of low-density parity-check codes for layered decoding algorithm and improve the decoding convergence speed, an improved layered decoding algorithm is proposed. In layered decoding algorithm, updated bit nodes information can be used by check nodes in the iteration process while in dynamic decoding algorithm check nodes update in order according to the reliability. The proposed algorithm combines advantages of the layered and dynamic decoding algorithm. Moreover, compared with the definition of remaining information for check nodes in the dynamic decoding algorithm, a new method to evaluate the reliability is defined in the proposed algorithm. Based on 1/2 code rate china mobile multimedia broadcasting standard, simulation and comparison between the conventional layered decoding algorithm and the proposed layered decoding algorithm have been carried out. The simulation results show that under the same bit error rate, the signal to noise ratio of the improved algorithm reduces nearly 0.4dB as well as convergence speed improves obviously. The proposed layered decoding algorithm reduces the bit error rate and improves the reliability of data in communication system which uses LDPC codes as the channel coding.