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Quantum communication is a growing interdisciplinary field which combines classical communications and quantum mechanics. Quantum error correction coding is one of the key techniques in quantum communication. Nearly all of the classical error correction coding schemes have been transplanted to the domain of quantum communication, and the quantum counterparts of classical error correction coding techniques have been found. Based on the classical turbo product codes (TPCs) which is one of the most outstanding schemes in classical coding region, a new structure of the CSS-type quantum convolutional codes (QCC) as stabilizer sub-code of the quantum turbo product codes (QTPC) is presented. Firstly, CSS-type QCC stabilizer generator is constructed with the help of group theory and the basic principle of stabilizer coders, and the corresponding networks are described. Secondly, the interleaved coded matrix of the QTPC is obtained by quantum permutation SWAP gate definition. Finally, the corresponding relation between the quantum trace distance of QTPC decoding and the distance of classical TPCs decoding is obtained, and the scheme of QTPCs coding and decoding is completed. The coding and decoding of QTPCs have a highly regular structure and a simple design idea, and the networks are easy to realize.
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Keywords:
- CSS coding /
- quantum convolutional codes /
- quantum turbo product codes /
- quantum error correcting coding
[1] Bennett C H 1992 Phys. Rev. Lett. 68 3124
[2] Xiao H L, Ouyang S, Nie Z P 2009 Acta Phys. Sin. 58 3685 (in Chinese) [肖海林、欧阳缮、聂在平 2009 58 3685]
[3] Xiao H L, Ouyang S, Nie Z P 2009 Acta Phys. Sin. 58 6779 (in Chinese) [肖海林、欧阳缮、聂在平 2009 58 6779]
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[5] Shor P W 1995 Phys. Rev. A 52 2493
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[7] Dave B 2008 Phys. Rev. A 78 042324
[8] Gottesman D 1996 Phys. Rev. A 54 1862
[9] Alexei A, Emanuel K 2001 IEEE Trans. Inf. Theory 47 3065
[10] Ashikhim A, Litsyn S, Tsfasman M 2001 IEEE Trans. Inf. Theory 47 1206
[11] David J C, Mitchison G, McFadden P L 2004 IEEE Trans. Inf. Theory 50 2315
[12] Xing L Z, Li Z, Bao B M, Wang X M 2008 Acta Phys. Sin. 57 4695 (in Chinese) [邢莉娟、李 卓、白宝明、王新梅 2008 57 4695]
[13] Yue K F, Zhao S M, Li M M 2008 Journal of Nanjing University of Posts and Telecomm 28 44 (in Chinese) [岳克峰、赵生妹、李苗苗 2008 南京邮电大学学报 28 44]
[14] Djordjevic I B 2009 IEEE Photonics Technology Lett. 21 842
[15] Vucetic B, Li Y H, Perez L C, Jiang F 2007 IEEE Proc. 95 1323
[16] Huebner A, Zigangirov K S, Costello D J 2008 IEEE Trans. Inf. Theory 54 3024
[17] Liese F, Vajda I 2006 IEEE Trans. Inf. Theory 52 4394
[18] Chen G T, Cao L, Yu Lun, Chen C W 2009 IEEE Trans. Comm. 57 307
[19] Xu C L, Liang Y C, Leon W S 2008 IEEE Trans. Wire. Comm. 7 43
[20] Calderbank A R, Shor P W 1996 Phys. Rev. A 54 1098
[21] Steane A M 1999 IEEE Trans. Inf. Theory 45 2492
[22] Fletcher A S, Shor P W, Win M Z 2008 IEEE Trans. Inf. Theory 54 5705
[23] Zhang Q, Tang C J, Gao F 2002 Acta Phys. Sin. 51 15 (in Chinese) [张 权、唐朝京、高 峰 2002 51 15]
[24] Jaromir F 2009 Phys. Rev. A 79 012330
[25] Heng F, Vwani R, Thomas S 2005 Phys. Rev. A 72 052323
[26] Zhang Q, Zhang E Y, Tang C J 2002 Acta Phys. Sin. 51 1676 (in Chinese) [张 权、张尔杨、唐朝京 2002 51 1676]
[27] Tetsufumi T, Liu Y X, Hu X D, Franco N 2009 Phys. Rev. Lett. 102 100501
[28] Zhang M, Dai H Y, Xi Z R, Xie H W, Hu D W 2007 Phys. Rev. A 76 042335
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[1] Bennett C H 1992 Phys. Rev. Lett. 68 3124
[2] Xiao H L, Ouyang S, Nie Z P 2009 Acta Phys. Sin. 58 3685 (in Chinese) [肖海林、欧阳缮、聂在平 2009 58 3685]
[3] Xiao H L, Ouyang S, Nie Z P 2009 Acta Phys. Sin. 58 6779 (in Chinese) [肖海林、欧阳缮、聂在平 2009 58 6779]
[4] Kremsky I, Hsieh M H, Brun T A 2008 Phys. Rev. A 78 012341
[5] Shor P W 1995 Phys. Rev. A 52 2493
[6] Calderbank A R, Shor P W 1996 Phys. Rev. A 54 1098
[7] Dave B 2008 Phys. Rev. A 78 042324
[8] Gottesman D 1996 Phys. Rev. A 54 1862
[9] Alexei A, Emanuel K 2001 IEEE Trans. Inf. Theory 47 3065
[10] Ashikhim A, Litsyn S, Tsfasman M 2001 IEEE Trans. Inf. Theory 47 1206
[11] David J C, Mitchison G, McFadden P L 2004 IEEE Trans. Inf. Theory 50 2315
[12] Xing L Z, Li Z, Bao B M, Wang X M 2008 Acta Phys. Sin. 57 4695 (in Chinese) [邢莉娟、李 卓、白宝明、王新梅 2008 57 4695]
[13] Yue K F, Zhao S M, Li M M 2008 Journal of Nanjing University of Posts and Telecomm 28 44 (in Chinese) [岳克峰、赵生妹、李苗苗 2008 南京邮电大学学报 28 44]
[14] Djordjevic I B 2009 IEEE Photonics Technology Lett. 21 842
[15] Vucetic B, Li Y H, Perez L C, Jiang F 2007 IEEE Proc. 95 1323
[16] Huebner A, Zigangirov K S, Costello D J 2008 IEEE Trans. Inf. Theory 54 3024
[17] Liese F, Vajda I 2006 IEEE Trans. Inf. Theory 52 4394
[18] Chen G T, Cao L, Yu Lun, Chen C W 2009 IEEE Trans. Comm. 57 307
[19] Xu C L, Liang Y C, Leon W S 2008 IEEE Trans. Wire. Comm. 7 43
[20] Calderbank A R, Shor P W 1996 Phys. Rev. A 54 1098
[21] Steane A M 1999 IEEE Trans. Inf. Theory 45 2492
[22] Fletcher A S, Shor P W, Win M Z 2008 IEEE Trans. Inf. Theory 54 5705
[23] Zhang Q, Tang C J, Gao F 2002 Acta Phys. Sin. 51 15 (in Chinese) [张 权、唐朝京、高 峰 2002 51 15]
[24] Jaromir F 2009 Phys. Rev. A 79 012330
[25] Heng F, Vwani R, Thomas S 2005 Phys. Rev. A 72 052323
[26] Zhang Q, Zhang E Y, Tang C J 2002 Acta Phys. Sin. 51 1676 (in Chinese) [张 权、张尔杨、唐朝京 2002 51 1676]
[27] Tetsufumi T, Liu Y X, Hu X D, Franco N 2009 Phys. Rev. Lett. 102 100501
[28] Zhang M, Dai H Y, Xi Z R, Xie H W, Hu D W 2007 Phys. Rev. A 76 042335
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