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Video Engineering

Improved Decoding Algorithm of LDPC Codes Based on Integer Operation

MA Huimia

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

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.

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Low-Density Parity check (LDPC) codes offer high-performance error correction near the Shannon limit which employs large code lengths and some iterations in the decoding process. The conventional decoding algorithm of LDPC is the Log Likelihood Ratio based Belief Propagation (LLR BP) which is also known as the `Sum-Product algorithm' which gives the best decoding performance and requires the most computational complexity and implementations with increased hardware complexity. Another simpler variant of this algorithm is used which is known as `min-sum algorithm' which reduces computational complexity as well as hardware complexity but with reduced accuracy. This paper analyzes the reason min-sum algorithm is more prone to errors when compared to the sum-product algorithm, and puts forward two improved algorithms which improve the performance of the min-sum algorithm with comparable algorithmic complexity.

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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.
Based on the investigation of the low-density parity-check(LDPC) codes' layered decoding algorithm in additive white Gaussian noise(AWGN) channel,an improved layered decoding algorithm based on integer operation is proposed for decoding LDPC codes.All the variables are indicated as integers in the proposed algorithm,so it is very convenient for implementation in hardware.At the same time,a modified factor is introduced to improve the layered decoding algorithm.With this modified factor,its decoding performance is improved greatly.Simulation results in AWGN channel show that the improved layered decoding algorithm can not only reduce the computation complexity and accelerate the convergence rate,but also have a lower error floor.
The LDPC codes decoding algorithm over additive white gaussian noise(AWGN) channels was studied,and a min-sum algorithm based on integer operation was proposed for decoding LDPC codes.All the variables were fixed length integers in this algorithm,which was very convenient for hardware implementation.At the signal-to-noise ratios(SNR) above 3dB,its performance was equal to that of sum-product algorithm whose variables were high precision floating point numbers.Also,a coefficient was designed to modify the min-sum algorithm,whose decoding performance was improved greatly especially at low SNR.And another achievement had been found that this algorithm had a lower error floor at high SNR.
Under the condition of the Additive White Gaussian Noise(AWGN) channel,both the hard and soft decision decoding algorithms suitable for LDPC codes are simulated and comparatively analyzed based on analyzing the decoding algorithm for LDPC codes.The variable message correlation for Log-Likelihood-Ratio Belief-Propagation(LLR-BP) algorithm in soft decision algorithm is decreased by introducing a multiplicative correction factor.The simulation results show that the decoding error-correction performance of the modified LLR-BP algorithm is greatly improved with little increase of computing complexity.
This paper proposes an adaptive normalized min-sum algorithm for the decoding of low-density parity check (LDPC) codes, which utilizes an adaptive normalization factor to improve the accuracy of the soft information transferred during the iterative decoding process, and provides superior performance accordingly. This adaptive normalization factor can be adjusted dynamically and adaptively at each decoding iteration according to a look-up table obtained via training and simulation. Its implementation facility and independence from the channel characteristics make the proposed adaptive normalized min-sum algorithm expect a wide application. Simulation results show that the proposed algorithm can achieve performance much closer to the sum-product algorithm and a coding gain of around 0.2dB compared to the conventional normalized min-sum algorithm for DVB-S2's rate 2/5 and 3/5 LDPC codes over the additive white Gaussian noise (AWGN) channel.
To improve performance and reduce computation complexity of the low-density parity-check (LDPC) codes, a min-sum based differential decoding algorithm is proposed. The main principle is that the messages passing in the bipartite graph of the codes are the probability differences and the updates of the check nodes adopt min sum algorithm. Simulation results show that the proposed algorithm can achieve about 0.4dB performance gain over the UMP BP-Based decoding algorithm at bit error rate (BER) of under an additive white Gaussian noise (AWGN) channel. And it can obtain good performance very close to that of the BP decoding algorithm with much lower complexity.
Low-Density Parity check (LDPC) codes offer high-performance error correction near the Shannon limit which employs large code lengths and some iterations in the decoding process. The conventional decoding algorithm of LDPC is the Log Likelihood Ratio based Belief Propagation (LLR BP) which is also known as the `Sum-Product algorithm' which gives the best decoding performance and requires the most computational complexity and implementations with increased hardware complexity. Another simpler variant of this algorithm is used which is known as `min-sum algorithm' which reduces computational complexity as well as hardware complexity but with reduced accuracy. This paper analyzes the reason min-sum algorithm is more prone to errors when compared to the sum-product algorithm, and puts forward two improved algorithms which improve the performance of the min-sum algorithm with comparable algorithmic complexity.