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Xiao, Hailin; Ni, Ju; Xie, Wu; Ouyang, Shan

A construction of quantum turbo product codes based on CSS-type quantum convolutional codes. (English) Zbl 1359.81097

Int. J. Quantum Inf. 15, No. 1, Article ID 1750003, 14 p. (2017).
Summary: As in classical coding theory, turbo product codes (TPCs) through serially concatenated block codes can achieve approximatively Shannon capacity limit and have low decoding complexity. However, special requirements in the quantum setting severely limit the structures of turbo product codes (QTPCs). To design a good structure for QTPCs, we present a new construction of QTPCs with the interleaved serial concatenation of CSS\((L_1,L_2)\)-type quantum convolutional codes (QCCs). First, CSS\((L_1,L_2)\)-type QCCs are proposed by exploiting the theory of CSS-type quantum stabilizer codes and QCCs, and the description and the analysis of encoder circuit are greatly simplified in the form of Hadamard gates and C-NOT gates. Second, the interleaved coded matrix of QTPCs is derived by quantum permutation SWAP gate definition. Finally, we prove the corresponding relation on the minimum Hamming distance of QTPCs associated with classical TPCs, and describe the state diagram of encoder and decoder of QTPCs that have a highly regular structure and simple design idea.

Cited in 1 Document

MSC:

81P70 Quantum coding (general)
94B10 Convolutional codes
94B25 Combinatorial codes

Keywords:

CSS-type stabilizer codes; quantum convolutional codes; quantum turbo product codes; quantum error-correcting codes
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References:

[1] Abu-Nada, A., Fortescue, B. and Byrd, M., Phy. Rev. A89 (2014) 062304.
[2] Cafaro, C., Maiolini, F. and Mancini, S., Phy. Rev. A86 (2012) 022308.
[3] Forney, G. D., Grassl, M. and Guha, S., IEEE Trans. Inf. Theory53 (2013) 865.
[4] Pelchat, E. and Poulin, D., IEEE Trans. Inf. Theory59 (2013) 3915. · Zbl 1364.81098
[5] Ollivier, H. and Tillich, J.-P., Phys. Rev. Lett.91 (2003) 177902.
[6] Wilde, M. M. and Brun, T. A., Quantum Inf. Process.9 (2010) 509. · Zbl 1200.81041
[7] Chen, J., Li, J., Yang, F. and Huang, Y., Int. J. Theor. Phys.54 (2015) 198. · Zbl 1315.81033
[8] Houshmand, M. and Wilde, M. M., IEEE Trans. Inf. Theory59 (2013) 6724. · Zbl 1364.81093
[9] Calderbank, A. R. and Shor, P. W., Phys. Rev. A54 (1996) 1098.
[10] Kasai, K., Hagiwara, M., Imai, H. and Sakaniwa, K., IEEE Trans. Inf. Theory58 (2012) 1223. · Zbl 1365.81041
[11] Fujiwara, Y. and Tonchev, V. D., IEEE Trans. Inf. Theory59 (2013) 3347. · Zbl 1364.81090
[12] Couvreur, A., Delfosse, N. and Zemor, G., IEEE Trans. Inf. Theory59 (2013) 6087. · Zbl 1364.81086
[13] Tillich, J.-P. and Zemor, G., IEEE Trans. Inf. Theory60 (2014) 1193. · Zbl 1364.94630
[14] Fern, J. and Whaley, K. B., Phys. Rev. A78 (2008) 062335.
[15] Shaw, B., Wilde, M. M., Oreshkov, O., Kremsky, I. and Lidar, D. A., Phys. Rev. A78 (2008) 12337.
[16] Poulin, D., Tillich, J.-P. and Ollivier, H., IEEE Trans. Inf. Theory55 (2009) 2776. · Zbl 1367.81043
[17] Tan, P. and Li, J., IEEE Trans. Inf. Theory56 (2009) 476.
[18] Xu, C., Liang, Y.-C. and Leon, W. S., IEEE Trans. Veh. Technol.56 (2007) 3495.
[19] Xiao, H., Ouyang, S. and Xie, W., Acta Phys.58 (2011) 6779.
[20] Fonseka, J. P., Dowling, E. M., Brown, T. K. and Han, S. I., IEEE Commun. Lett.16 (2012) 1365.
[21] Argon, C. and Mclaughlin, S. W., IEEE Trans. Commun.52 (2006) 896.
[22] Wilde, M. M., Hsieh, M. H. and Babar, Z., IEEE Trans. Inf. Theory60 (2014) 1203. · Zbl 1364.81101
[23] Iblisdir, S., Assche, G. V. and Cerf, N. J., Phys. Rev. Lett.93 (2004) 170502.
[24] Wilde, M. M., Phys. Rev. A79 (2009) 062325.
[25] Argon, C. and McLaughlin, S. W., IEEE Commun. Lett.6 (2005) 70.
[26] MacKay, D. J. C., Mitchison, G. and McFadden, P., IEEE Trans. Inf. Theory50 (2004) 2315. · Zbl 1315.94145
[27] Djordjevic, I. B., IEEE Photon. J.2 (2010) 81.
[28] J. Rahhal, D. Abu-Al-Nadi and M. Hawa, Evolutional computation in coded communications: An implementation of viterbi algorithm, in IEEE Congr. Evolutionary Computation.
[29] Fonseka, J. P., Dowling, E. M., Han, S. I. and Hu, Y., IEEE Commun. Lett.17 (2013) 1431.
[30] Daneshgaran, F., Laddomada, M. and Mondin, M., IEEE Trans. Inf. Theory50 (2004) 1177. · Zbl 1293.94117
[31] Fan, H., Roychowdhury, V. and Szkopek, T., Phys. Rev. A72 (2005) 052323.
[32] Fiurasek, J., Phys. Rev. A79 (2009) 012330.
[33] Walton, Z. D., Abouraddy, A. F., Sergienko, A. V., Saleh, B. E. A. and Teich, M. C., Phys. Rev. Lett.91 (2009) 087901.
[34] Xiao, H. and Ouyang, S., J. Appl. Phys.112 (2012) 34903.
[35] Tanamoto, T., Liu, Y., Hu, X. and Nori, F., Phys. Rev. Lett.102 (2009) 100501.
[36] Cafaro, C. and van Loock, P., Phys. Rev. A89 (2014) 022316.
[37] Chau, H. F., Phys. Rev. A60 (1999) 1966.
[38] Zhang, M., Dai, H. Y., Xi, Z., Xie, H. W. and Hu, D., Phys. Rev. A76 (2007) 042335.
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