基于密度进化理论改进的LDPC码偏移最小和算法
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摘要
针对目前LDPC码偏移最小和算法的偏移因子的选取方式不够准确灵活等问题,提出了一种基于密度进化理论改进的最小和算法,称为DOMS算法。该算法首先根据密度进化理论计算BP算法和MS算法在每次迭代译码过程中,校验节点传递给变量节点的信息的概率质量函数,然后由两者的差值得出每次迭代对应的偏移因子β_m,m表示第m次迭代。再对偏移因子序列β_m做加权平均处理得到新的偏移因子β。通过使用该偏移因子,DOMS算法与经典的OMS算法相比,仿真结果表明大约可以取得0.2 dB的增益。此外,当对比与BP算法译码性能相近的LMMSE Min Sum算法时,DOMS算法在获得相似译码性能的基础上,可以节省大约28.29%的逻辑元器件和34.33%的内存。
The offset factor used by Offset Min-Sum(OMS)algorithm of Low-Density Parity-Check(LDPC)codes is not accuracy currently. This paper proposed an improved Min-Sum(MS)algorithm based on Density Evolution(DE)theory,called the DE-based Offset Min Sum(DOMS)algorithm. The algorithm uses DE theory to calculate the Probability Mass Function(PMF)of check-to-variable(C2 V)messages in Belief Propagation(BP)algorithm and Min Sum algorithm,and then obtain the offset factors sequence β_m by calculating the difference between them,where m represents the m-th iteration. Finally,the β needed is obtained by doing a weighted average of β_m. By using this offset factor β,the DOMS algorithm will have a gain of about 0.2 dB compared to the classical OMS algorithm. In addition,compared with LMMSE Min Sum algorithm whose decoding performance is very close to BP algorithm,the DOMS algorithm can save about 28.29% of logic elements and 34.33% of memory bits within similar performance.
The offset factor used by Offset Min-Sum(OMS)algorithm of Low-Density Parity-Check(LDPC)codes is not accuracy currently. This paper proposed an improved Min-Sum(MS)algorithm based on Density Evolution(DE)theory,called the DE-based Offset Min Sum(DOMS)algorithm. The algorithm uses DE theory to calculate the Probability Mass Function(PMF)of check-to-variable(C2 V)messages in Belief Propagation(BP)algorithm and Min Sum algorithm,and then obtain the offset factors sequence β_m by calculating the difference between them,where m represents the m-th iteration. Finally,the β needed is obtained by doing a weighted average of β_m. By using this offset factor β,the DOMS algorithm will have a gain of about 0.2 dB compared to the classical OMS algorithm. In addition,compared with LMMSE Min Sum algorithm whose decoding performance is very close to BP algorithm,the DOMS algorithm can save about 28.29% of logic elements and 34.33% of memory bits within similar performance.
引文
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[14] Wang Xiumin,Cao Weilin,Li Jun,et al.Improved Min-Sum Algorithm Based on Density Evolution for Low-Density Parity Check Codes[J].IET Communications,2017,11(10):1582-1586
[2] Mackay D J C.Good Error-Correcting Codes Based on Very Sparse Matrices[J].IEEE Transactions on Information Theory,1999,45(2):399-431.
[3] Fowdur T P,Furzun B N.Performance of IEEE 802.11n LDPC Codes with Modified Reliability-Based Hybrid ARQ and Unequal Error Protection[C]//Eurocon 2015-International Conference on Computer as A Tool.IEEE,2015:1-6.
[4] IEEE Standards Association,IEEE Standard P802.16e-2005:Part 16:Air Interface for Fixed and Mobile Broadband Wireless Access Systems Amendment for Physical and Medium[S].IEEE-SA,Piscataway(2005):501-510.
[5] Xu M,Ji X,Wu J,et al.A Modified BP Algorithm for LDPC Decoding Based on Minimum Mean Square Error Criterion[J].Ieice Transactions on Communications,2010,93(5):1256-1259.
[6] 尹晓琦,Yin Xiaoqi.基于密度进化算法的正则LDPC码噪声门限[J].河北大学学报(自然科学版),2016,36(3):332-336.
[7] Fossorier M P C,Mihaljevic M,Imai H.Reduced Complexity Iterative Decoding of Low-Density Parity Check Codes Based on Belief Propagation[J].IEEE Transactions on Communications,2002,47(5):673-680.
[8] Chen J,Fossorier M P C.Density Evolution for Two Improved BP-Based Decoding Algorithms of LDPC Codes[J].IEEE Communications Letters,2002,6(5):208-210.
[9] Cao Y.An Improved LDPC Decoding Algorithm Based on Min-Sum Algorithm[C]//International Symposium on Communications and Information Technologies.IEEE,2011:26-29.
[10] Xu M,Wu J,Zhang M.A Modified Offset Min-Sum Decoding Algorithm for LDPC Codes[C]//IEEE International Conference on Computer Science and Information Technology.IEEE,2010:19-22.
[11] Wu Z,Su K,Guo L.A Modified Min Sum Decoding Algorithm Based on LMMSE for LDPC Codes[J].AEU-International Journal of Electronics and Communications,2014,68(10):994-999.
[12] Ngassa C K,Savin V,Dupraz E,et al.Density Evolution and Functional Threshold for the Noisy Min-Sum Decoder[J].IEEE Transactions on Communications,2014,63(5):1497-1509.
[13] Richardson T J,Urbanke R L.The Capacity of Low-Density Parity-Check Codes under Message-Passing Decoding[M].IEEE Press,2001.
[14] Wang Xiumin,Cao Weilin,Li Jun,et al.Improved Min-Sum Algorithm Based on Density Evolution for Low-Density Parity Check Codes[J].IET Communications,2017,11(10):1582-1586