简化的Log-BP迭代译码算法的研究

发布时间：2018-07-20 16:33

【摘要】：低密度奇偶校验码(LDPC,Low Density Parity-Check Codes)和已经实际应用的Turbo码相比,有其独特的优势。近年来LDPC码得到了广泛的关注和研究,并且将应用于越来越多的通信系统中。在LDPC码的译码算法中,Log-BP算法是性能最好的。但是在Log-BP算法中校验节点更新的过程中,需要计算双曲正切函数tanh(x)和反双曲正切函数1tanh(x)?,这两个函数的计算极大地增加了算法的复杂度。本文对于降低双曲正切函数和反双曲正切函数复杂度的SSP(Simplified Sum-Product algorithm)算法进行了性能仿真和分析。本文在此基础上提出了基于等弦长直线简化的Log-BP算法。由于直线逼近曲线的误差选取的不同,直线的选择也就不同。本文对于等弦长简化算法采用的误差为0.02和0.095,为了能与SSP算法的性能进行直观的比较,因此等弦长简化算法选取的最少的直线条数为九条,对应的误差为0.095。除此之外本文还提出了基于等间距直线简化的Log-BP算法。由于直线逼近曲线的误差选取的不同,直线的选择也就不同。本文对于等间距简化算法采用的误差为0.022和0.195,为了能与SSP算法的性能进行直观的比较,因此等间距简化算法选取的最少的直线条数为九条,对应的误差为0.195。另外为了与误差为0.02的等弦长简化算法的直线条数对应起来,因此选用的等间距简化算法的误差为0.022。本文对原始的Log-BP算法,SSP算法,等弦长简化的Log-BP算法,等间距简化的Log-BP算法进行了仿真。从性能仿真结果上可以看出,SSP算法,等弦长简化算法和等间距简化算法的性能要比原始的Log-BP算法的性能要差一些。总体上,等弦长简化算法和等间距算法在选取直线条数一样的情况下要比SSP算法的性能要好一些。对于等弦长简化算法和等间距简化算法来说,总体上等间距简化算法要比等弦长简化算法的性能要好一些。虽然这两种简化算法的性能与原始的Log-BP算法的性能在高性噪比的条件下有一些差距,但是从这两种简化算法所能带来的复杂度的降低来看,这点性能的损失是值得的。
[Abstract]:LDPC low density Parity-Check codes (LDPC codes) have unique advantages over Turbo codes which have been applied in practice. In recent years, LDPC codes have received extensive attention and research, and will be used in more and more communication systems. Among the decoding algorithms of LDPC codes, Log-BP algorithm is the best. However, in the process of checking node updating in Log-BP algorithm, it is necessary to calculate the hyperbolic tangent function tanh (x) and the inverse hyperbolic tangent function 1tanh (x), which greatly increase the complexity of the algorithm. In this paper, the performance of SSP (simplified Sum-Product algorithm) algorithm which reduces the complexity of hyperbolic tangent function and anti-hyperbolic tangent function is simulated and analyzed. In this paper, a simplified Log-BP algorithm based on equal-chord length straight line is proposed. Because of the difference of the error selection of the line approximation curve, the choice of the straight line is also different. In this paper, the error of equal-chord length simplification algorithm is 0.02 and 0.095. In order to compare directly with the performance of SSP algorithm, the minimum number of straight lines and the corresponding error of equal-chord length simplification algorithm are 9 and 0.095 respectively. In addition, this paper proposes a Log-BP algorithm based on equal-distance line simplification. Because of the difference of the error selection of the line approximation curve, the choice of the straight line is also different. In this paper, the error of the equal-spacing simplification algorithm is 0.022 and 0.195. In order to compare directly with the performance of the equal-spacing simplification algorithm, the minimum number of straight lines and the corresponding error of the equal-spacing simplification algorithm are nine and 0.195 respectively. In addition, in order to correspond to the number of straight lines of the equal-chord length simplification algorithm with an error of 0.02, the error of the equal-spacing simplification algorithm is 0.022. This paper simulates the original Log-BP algorithm SSP algorithm, the equal-chord length simplified Log-BP algorithm and the equal-spacing simplified Log-BP algorithm. It can be seen from the simulation results that the performance of the SSP algorithm, the equal-chord length simplification algorithm and the equal-spacing simplification algorithm is worse than that of the original Log-BP algorithm. In general, the performance of the equal-chord length simplification algorithm and the equal-spacing algorithm is better than that of the SSP algorithm when the number of straight lines is the same. For the equal-chord length simplification algorithm and the equal-spacing simplification algorithm, the performance of the equal-space simplification algorithm is better than that of the equal-chord length simplification algorithm. Although the performance of these two simplified algorithms is somewhat different from that of the original Log-BP algorithm under the condition of high performance noise ratio, the performance loss of these two simplified algorithms is worth considering from the reduction of complexity brought by these two simplified algorithms.
【学位授予单位】：西安电子科技大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TN911.22

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