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Hans Journal of Wireless Communications

LDPC Sum-Product Decoding Based on Synchronized Information

洋洋 陈

Published Jan 1, 2015• 0 citations
Publisher

Abstract

低密度奇偶校验码(LDPC)是一类具有稀疏校验矩阵的线性分组码，和积算法是理论可行的LDPC软解码算法，但其实用受制于计算复杂度。最小和算法及其它已知改进算法采用近似来有效简化每次迭代的过程，以部分性能为代价，在一定程度上弥补了前述缺陷。本文提出了基于同步信息修正的和积算法，在保持原算法每次迭代复杂度以保证性能的前提下，利用同步信息对算法进行修正，有效减少了算法迭代次数，因此降低了计算复杂度，提高了实用性。Low density parity check code (LDPC) is a subclass of linear block code with sparse check matrix. Sum-product algorithm is efficient for decoding LDPC theoretically, but not practically due to its complexity. Improved algorithms including minimum sum algorithm reduce computational com-plexity by approximation but performance is degraded. In this paper, we introduce corrected sum-product algorithm based on synchronized information, which improves the practicability by reducing the iterations without performance degradation.

DOI
10.12677/hjwc.2015.53010

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低密度奇偶校验码(LDPC)是一类具有稀疏校验矩阵的线性分组码，和积算法是理论可行的LDPC软解码算法，但其实用受制于计算复杂度。最小和算法及其它已知改进算法采用近似来有效简化每次迭代的过程，以部分性能为代价，在一定程度上弥补了前述缺陷。本文提出了基于同步信息修正的和积算法，在保持原算法每次迭代复杂度以保证性能的前提下，利用同步信息对算法进行修正，有效减少了算法迭代次数，因此降低了计算复杂度，提高了实用性。Low density parity check code (LDPC) is a subclass of linear block code with sparse check matrix. Sum-product algorithm is efficient for decoding LDPC theoretically, but not practically due to its complexity. Improved algorithms including minimum sum algorithm reduce computational com-plexity by approximation but performance is degraded. In this paper, we introduce corrected sum-product algorithm based on synchronized information, which improves the practicability by reducing the iterations without performance degradation.
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.
The sum-product iterative decoder, conventionally used for low-density parity-check (LDPC) codes, hold promise as a decoder for general linear block code decoding. However, the promise is only partly fulfilled because, as we show experimentally, the decoder performance degrades rapidly as a function of parity check matrix weight. Even in the case of decoder failure, however, we demonstrate that there is information present in the decoder output probabilities that can still help with the decoding problem.
Low-density parity-check (LDPC) codes are a subclass of linear block codes. These codes have parity-check matrices in which the ratio of the non-zero elements to all elements is low. This property is exploited in defining low complexity decoding algorithms. Low-density parity-check codes have good distance properties and error correction capability near Shannon limits. In this thesis, the sum-product and the bit-flip decoding algorithms for low-density parity-check codes are implemented on Intel Pentium M 1,86 GHz processor using the software called MATLAB. Simulations for the two decoding algorithms are made over additive white gaussian noise (AWGN) channel changing the code parameters like the information rate, the blocklength of the code and the column weight of the parity-check matrix. Performance comparison of the two decoding algorithms are made according to these simulation results. As expected, the sum-product algorithm, which is based on soft-decision decoding, outperforms the bit-flip algorithm, which depends on hard-decision decoding. Our simulations show that the performance of LDPC codes improves with increasing blocklength and number of iterations for both decoding algorithms. Since the sum-product algorithm has lower error-floor characteristics, increasing the number of iterations is more effective for the sum-product decoder compared to the bit-flip decoder. By having better BER performance for lower information rates, the bit-flip algorithm performs according to the expectations; however, the performance of the sum-product decoder deteriorates for information rates below 0.5 instead of improving. By irregular construction of LDPC codes, a performance improvement is observed especially for low SNR values.
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.
An improved parallel decoding approach of sum-product algorithm for low-density parity-check codes(LDPC) was presented in order to solve the problem of divergence in decoding iteration with finite precision,.In addition,the reason for improving the convergence speed was discussed detailedly and the pipeline structure was provided.By eliminating the unexpected state in which operation data didn't satisfy input rules due to the finite precision effect thus could not be preceded correctly,the iteration convergence was improved efficiently and led to decoding with no error.Compared with the original parallel approach,this improvement don't involve too much control logic and computational complexity.Simulation shows that the proposed decoding approach over additive white Gaussian noise(AWGN) channel achieves good performance,especially at high code rate,it suffers negligible performance loss compared with the forward-backward approach while reducing the operation complexity effectively.