基于极大极小准则下的(n,k,m)卷积码识别
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摘要
针对现有识别方法仅适用于特定类型的卷积码,以及容错能力有待提高的问题,提出了一种基于改进门限沃尔什-哈达玛变换(Walsh-Hadamard transform,WHT)的(n,k,m)卷积码参数遍历识别方法。首先,将问题分为非系统和系统形式两种情况进行考虑,根据各自结构特点分别建立关于校验多项式的二元域方程,并建立二元假设;然后,遍历不同的参数组合并利用WHT求解对应方程,通过二元判决得到校验多项式,同时为提升方法的鲁棒性,采用极大极小准则对判决门限进行了改进。最后,利用校验多项式矩阵与生成多项式矩阵的正交关系求解生成多项式。仿真结果表明,该方法对各码率的卷积码均能有效识别,且抗误码性能优于传统方法。
Current recognition methods for convolutional codes are only applicable to a specific code rate,and fault tolerant performance needs to be improved as well.To solve this problem,aparameter method based on parameter traversal and improved threshold Walsh-Hadamard transform(WHT)is proposed.According to the coding structure,F(2)equations for check polynomials are established in both cases of nonsystematic and systematic codes,with binary hypothesis being established.By traversing the possible coding parameters and solving the equations via WHT,the correct check polynomials are determined through threshold decision,while the threshold is improved based on maximum and minimum criterion to enhance robustness at the same time.Finally,generator polynomials are calculated on the basis of orthogonal relationship between check matrix and generator matrix.Simulations verify the applicability of the proposed method,which has a better error resilient performance compared with current recognition methods.
Current recognition methods for convolutional codes are only applicable to a specific code rate,and fault tolerant performance needs to be improved as well.To solve this problem,aparameter method based on parameter traversal and improved threshold Walsh-Hadamard transform(WHT)is proposed.According to the coding structure,F(2)equations for check polynomials are established in both cases of nonsystematic and systematic codes,with binary hypothesis being established.By traversing the possible coding parameters and solving the equations via WHT,the correct check polynomials are determined through threshold decision,while the threshold is improved based on maximum and minimum criterion to enhance robustness at the same time.Finally,generator polynomials are calculated on the basis of orthogonal relationship between check matrix and generator matrix.Simulations verify the applicability of the proposed method,which has a better error resilient performance compared with current recognition methods.
引文
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[15]谢辉,王丰华,黄知涛,等.基于改进欧几里得算法的卷积码快速盲识别算法[J].国防科技大学学报,2012,34(6):158-162.XIE H,WANG F H,HUANG Z T,et al.A fast method for blind recognition of convolutional codes based on improved Euclidean algorithm[J].Journal of National University of Defense Technology,2012,34(6):158-162.
[16]刘健,王晓君,周希元.基于Walsh-Hadamard变换的卷积码盲识别[J].电子与信息学报,2010,32(4):884-888.LIU J,WANG X J,ZHOU X Y.Blind recognition of convolutional coding based on Walsh-Hadamard transform[J].Journal of Electronics&Information Technology,2010,32(4):884-888.
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[18]XIONG Y.Convolutional code blind recognition model considering generalized coupling dark information[J].Boletín Técnico,2017,55(5):131-139.
[19]LIN S,COSTELLO D.Error control coding[M].2nd ed.New Jersey,USA:Prentice Hall,2005:300-321.
[20]JOHANNESSON R,ZIGANGIROV K.Fundamentals of convolutional coding[M].New Jersey,USA:Wiley,2015:49-150.
[2]MUKHTAR H,ALDWEIK A,SHAMI A.Turbo product codes:applications,challenges,and future directions[J].IEEECommunications Surveys&Tutorials,2016,18(4):3052-3069.
[3]谢辉,黄知涛,王峰华.信道编码盲识别技术研究进展[J].电子学报,2013,41(6):1166-1176.XIE H,HUANG Z T,WANG F H.Research progress of blind recognition of channel coding[J].ACTA Electronica Sinica,2013,41(6):1166-1176.
[4]MOOSAVI R,LARSSON E G.Fast blind recognition of channel codes[J].IEEE Trans.on Communications,2014,62(5):1393-1405.
[5]CHEN W G,WU G Q.Blind recognition of(n-1)/nrate punctured convolutional encoders in a noisy environment[J].Journal of Communications,2015,10(4):260-267.
[6]YARDI A D,VIJAYKUMARAN S,KUMAR A.Blind reconstruction of binary cyclic codes from unsynchronized bit stream[J].IEEE Trans.on Communications,2016,64(7):2693-2706.
[7]张立民,吴昭军,钟兆根.一种基于遗传算法的RSC码盲识别方法[J].航空学报,2017,38(11):277-286.ZHANG L M,WU Z J,ZHONG Z G.Blind identification of RSC code based on genetic algorithm[J].Acta Aeronautica et Astronautica Sinica,2017,38(11):277-286.
[8]MARAZIN M,GAUTIER R,BUREL G.Blind recovery of k/n rate convolutional encoders in a noisy environment[J].EURASIPJournal on Wireless Communications and Networking,2011:10.1186/1687-1499-2011-168.
[9]ZRELLI Y,GAUTIER R,MARAZIN M,et al.Focus on theoretical properties of blind convolutional codes identification methods based on rank criterion[C]∥Proc.of the IEEE International Conference on Communications,2012:353-356.
[10]SOTEH A,BIZAKI H.On the analytical solution of rank problem in the convolutional code identification context[J].IEEE Communications Letters,2016,20(3):442-445.
[11]YAO W,WANG F,HUANG Z.Blind recognition of(n,k,m)convolutional code based on local decision in a noisy environment[C]∥Proc.of the International Conference on Automation,Mechanical Control and Computational Engineering,2015:554-559.
[12]HUANG L,CHEN W G,CHEN E,et al.Blind recognition of k/n rate convolutional encoders from noisy observation[J].Journal of Systems Engineering and Electronics,2017,28(2):235-243.
[13]LU P Z,ZOU Y.Fast computations of Grobner bases and blind recognitions of convolutional codes[J].Lecture Notes in Computer Science,2007,4547:303-317.
[14]WANG F H,HUANG Z T,ZHOU Y.A method for blind recognition of convolution code based on Euclidean algorithm[C]∥Proc.of the IEEE International Conference on Wireless Communications,Networking and Mobile Computing,2007:1414-1417.
[15]谢辉,王丰华,黄知涛,等.基于改进欧几里得算法的卷积码快速盲识别算法[J].国防科技大学学报,2012,34(6):158-162.XIE H,WANG F H,HUANG Z T,et al.A fast method for blind recognition of convolutional codes based on improved Euclidean algorithm[J].Journal of National University of Defense Technology,2012,34(6):158-162.
[16]刘健,王晓君,周希元.基于Walsh-Hadamard变换的卷积码盲识别[J].电子与信息学报,2010,32(4):884-888.LIU J,WANG X J,ZHOU X Y.Blind recognition of convolutional coding based on Walsh-Hadamard transform[J].Journal of Electronics&Information Technology,2010,32(4):884-888.
[17]SU S J,ZHOU J,HUANG Z T,et al.Blind identification of convolutional encoder parameters[J].The Scientific World Journal,2014:10.1155/2014/798612.
[18]XIONG Y.Convolutional code blind recognition model considering generalized coupling dark information[J].Boletín Técnico,2017,55(5):131-139.
[19]LIN S,COSTELLO D.Error control coding[M].2nd ed.New Jersey,USA:Prentice Hall,2005:300-321.
[20]JOHANNESSON R,ZIGANGIROV K.Fundamentals of convolutional coding[M].New Jersey,USA:Wiley,2015:49-150.