Nearly perfect Gaussian integer sequences with arbitrary degree

Yubo Li; Liying Tian; Tao Liu

Nearly perfect Gaussian integer sequences with arbitrary degree

View Fulltext

Author(s): Yubo Li^{1, 2} ; Liying Tian^{1, 2} ; Tao Liu^{1, 2}
- Affiliations: 1: School of Information Science and Engineering , Yanshan University , Qinhuangdao 066004, Hebei , People's Republic of China ;
  2: Hebei Key Laboratory of Information Transmission and Signal Processing , Qinhuangdao 066004, Hebei , People's Republic of China
Source: Volume 12, Issue 9, 05 June 2018, p. 1123 – 1127
DOI: 10.1049/iet-com.2017.1274 , Print ISSN 1751-8628, Online ISSN 1751-8636

Received 12/11/2017, Accepted 16/02/2018, Revised 13/01/2018, Published 23/02/2018

Based on p-ary pseudorandom sequences, this study proposes a construction of degree-k Gaussian integer sequences of period $N = k ( p m − 1 ) / ( p − 1 )$ by utilising kth power residue symbol satisfying $k | ( p − 1 )$ , where p is an odd prime and positive integers $m , k ≥ 2$ . The periodic autocorrelation values are 0 at shifts $τ ≢ 0 ( mod ( N / k ) )$ of the resultant sequences. Specially, there is exactly one non-zero out-of-phase periodic autocorrelation value of the resultant sequences for $k = 2$ . The non-zero elements of the sequences are balanced and can be predefined flexibly. Moreover, the maximum energy efficiency of the proposed sequences is close to $( p − 1 ) / p$ for sufficiently large m.

References

1. 1)
  - 22. Lee, C.D., Hong, S.: ‘Generation of long perfect Gaussian integer sequences’, IEEE Signal Process. Lett., 2017, 24, (4), pp. 515–519.
2. 2)
  - 21. Chang, H.H.: ‘Degree-(k+1) perfect Gaussian integer sequences of period pk’, Proc. IEEE Int. Symp. Inf. Theory, Aachen, Germany, 2017, pp. 1505–1509.
3. 3)
  - 24. Fan, P.Z., Darnell, M.: ‘Sequence design for communications applications’ (Research Studies, London, UK, 1996).
4. 4)
  - 6. Huber, K.: ‘Codes over Gaussian integers’, IEEE Trans. Inf. Theory, 1994, 40, (1), pp. 207–216.
5. 5)
  - 4. Fan, P.Z., Marnell, D.: ‘Maximal length sequences over Gaussian integers’, Electron. Lett., 1994, 30, (16), pp. 1278–1286.
6. 6)
  - 25. Nogami, Y., Uehara, S., Tsuchiya, K., et al: ‘A multi-value sequence generated by power residue symbol and trace function over odd characteristic field’, IEICE Trans. Fundam. Electr. Commun. Comput. Sci., 2016, E99-A, (12), pp. 2226–2237.
7. 7)
  - 18. Lee, C.D., Chen, Y.H.: ‘Families of Gaussian integer sequences with high energy efficiency’, IET Commun., 2016, 10, (17), pp. 2416–2421.
8. 8)
  - 7. Li, C.P., Wang, S.H., Wang, C.L.: ‘Novel low-complexity SLM schemes for PAPR reduction in OFDM systems’, IEEE Trans. Signal Process., 2010, 58, (5), pp. 2916–2921.
9. 9)
  - 23. Golomb, S.W., Gong, G.: ‘Signal design for good correlation: for wireless communication, cryptography and radar’ (Cambridge University Press, Cambridge, UK, 2005).
10. 10)
  - 5. Deng, X., Fan, P.Z., Suehiro, N.: ‘Sequences with zero correlation over Gaussian integers’, Electron. Lett., 2000, 36, (6), pp. 552–553.
11. 11)
  - 1. Luke, H.D., Hadinejad, M.H.: ‘Binary and quadriphase sequences with optimal autocorrelation properties: a survey’, IEEE Trans. Inf. Theory, 2003, 49, (12), pp. 3271–3282.
12. 12)
  - 11. Yang, Y., Tang, X.H., Zhou, Z.C.: ‘Perfect Gaussian integer sequences of odd prime length’, IEEE Signal Process. Lett., 2012, 19, (10), pp. 615–618.
13. 13)
  - 19. Pei, S.C., Chang, K.W.: ‘Perfect Gaussian integer sequences of arbitrary length’, IEEE Signal Process. Lett., 2015, 22, (8), pp. 1040–1044.
14. 14)
  - 14. Lee, C.D., Huang, Y.P., Chang, Y., et al: ‘Perfect Gaussian integer sequences of odd period 2m−1’, IEEE Signal Process. Lett., 2015, 22, (7), pp. 881–885.
15. 15)
  - 17. Boztas, S., Parampalli, U.: ‘Nonbinary sequences with perfect and nearly perfect autocorrelations’, Proc. IEEE Int. Sym. Inf. Theory, Austin, Texas, USA, 2010, pp. 1300–1304.
16. 16)
  - 16. Chen, X., Li, C., Rong, C.: ‘Perfect Gaussian integer sequences from cyclic difference sets’, Proc. IEEE Int. Symp. Inf. Theory, Barcelona, Spain, 2016, pp. 115–119.
17. 17)
  - 12. Ma, X.W., Wen, Q.Y., Zhang, J., et al: ‘New perfect Gaussian integer sequences of period pq’, IEICE Trans. Fundam. Electr. Commun. Comput. Sci., 2013, E96-A, (11), pp. 2290–2293.
18. 18)
  - 9. Lusina, P., Shavgulidze, S., Bossert, M.: ‘Space-time block factorisation codes over Gaussian integers’, Proc. Inst. Elect. Eng. Commun., 2004, 151, (5), pp. 415–421.
19. 19)
  - 13. Chang, H.H., Li, C.P., Lee, C.D., et al: ‘Perfect Gaussian integer sequences of arbitrary composite length’, IEEE Trans. Inf. Theory, 2015, 61, (7), pp. 4107–4115.
20. 20)
  - 8. Wang, S.H., Li, C.P., Lee, K.C., et al: ‘A novel low-complexity precoded OFDM system with reduced PAPR’, IEEE Trans. Signal Process., 2015, 63, (6), pp. 1366–1376.
21. 21)
  - 20. Wang, S.H., Li, C.P., Chang, H.H., et al: ‘A systematic method for constructing sparse Gaussian integer sequences with ideal periodic autocorrelation functions’, IEEE Trans. Commun., 2016, 64, (1), pp. 365–376.
22. 22)
  - 2. Hoholdt, T., Justesen, J.: ‘Ternary sequences with perfect periodic autocorrelation’, IEEE Trans. Inf. Theory, 1983, 29, (4), pp. 597–600.
23. 23)
  - 3. Popovic, B.M.: ‘Generalized chirp-like polyphase sequences with optimum correlation properties’, IEEE Trans. Inf. Theory, 1992, 38, (4), pp. 1406–1409.
24. 24)
  - 10. Hu, W., Wang, S.H., Li, C.P.: ‘Gaussian integer sequences with ideal periodic autocorrelation functions’, IEEE Trans. Signal Process., 2012, 60, (11), pp. 6074–6079.
25. 25)
  - 15. Lee, C.D., Li, C.P., Chang, H.H., et al: ‘Further results on degree-2 perfect Gaussian integer sequences’, IET Commun., 2016, 10, (12), pp. 1542–1552.

Login

Not registered yet?

Share

Tools

Login to add to favourites

Key

Nearly perfect Gaussian integer sequences with arbitrary degree

References

Related content