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New CRT sequence sets for a collision channel without feedback

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Abstract

Protocol sequences are binary and periodic sequences used for deterministic multiple access in a collision channel without feedback. In this paper, we focus on user-irrepressible (UI) protocol sequences that can guarantee a positive individual throughput per sequence period with probability one for a slot-synchronous channel, regardless of the delay offsets among the users. As the sequence period has a fundamental impact on the worst-case channel access delay, a common objective of designing UI sequences is to make the sequence period as short as possible. Consider a communication channel that is shared by M active users, and assume that each protocol sequence has a constant Hamming weight w. To attain a better delay performance than previously known UI sequences, this paper presents a CRTm construction of UI sequences with \(w=M+1\), which is a variation of the previously known CRT construction. For all non-prime \(M\ge 8\), our construction produces the shortest known sequence period and the shortest known worst-case delay of UI sequences. Numerical results show that the new construction enjoys a better average delay performance than the optimal random access scheme and other constructions with the same sequence period, in a variety of traffic conditions. In addition, we derive an asymptotic lower bound on the minimum sequence period for \(w=M+1\) if the sequence structure satisfies some technical conditions, called equi-difference, and prove the tightness of this lower bound by using the CRTm construction.

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References

  1. Massey, J. L., & Mathys, P. (1985). The collision channel without feedback. IEEE Transactions on Information Theory, 31(2), 192–204.

    Article  MathSciNet  MATH  Google Scholar 

  2. Wong, W. S. (2007). New protocol sequences for random access channels without feedback. IEEE Transactions on Information Theory, 53(6), 2060–2071.

    Article  MathSciNet  MATH  Google Scholar 

  3. Chen, C. S., Wong, W. S., & Song, Y. Q. (2008). Constructions of robust protocol sequences for wireless sensor and ad hoc networks. IEEE Transactions on Vehicular Technology, 57(5), 3053–3063.

    Article  Google Scholar 

  4. Shum, K. W., Chen, C. S., Sung, C. W., & Wong, W. S. (2009). Shift-invariant protocol sequences for the collision channel without feedback. IEEE Transactions on Information Theory, 55(7), 3312–3322.

    Article  MathSciNet  MATH  Google Scholar 

  5. Wu, Y., Shum, K. W., Lin, Z., Wong, W. S., & Shen, L. (2013). Protocol sequences for mobile ad hoc networks. In Proceedings of IEEE international conference on communication, Budapest (pp. 1730–1735).

  6. Wu, Y., Shum, K. W., Wong, W. S., & Shen, L. (2014). Safety messages broadcast in vehicular ad hoc networks based on protocol sequences. IEEE Transactions on Vehicular Technology, 63(3), 1467–1479.

    Article  Google Scholar 

  7. Wong, W. S. (2014). Transmission sequence design and allocation for wide area ad hoc networks. IEEE Transactions on Vehicular Technology, 63(2), 869–878.

    Article  Google Scholar 

  8. Mao, Y., & Shen, L. (2016). A framework for protocol sequence allocation in vehicular ad hoc networks. In Proceedings of IEEE vehicular technology conference, Nanjing, China

  9. Xu, Z., Cai, L., & Wu, Y. (2016). Channel access mechanism based on equally allocation of protocol sequence for VANET. Journal on Communication, 37(4), 74–86.

    Google Scholar 

  10. Chen, C.-C., Yang, G.-C., Chang, M.-K., Lin, J.-S., Wong, W. S., & Kwong, W. C. (2016). Constructions and throughput analyses of protocol sequences with adjustable duty factor for collision channels without Feedback. IEEE Transaction on Communication, 65(10), 4736–4748.

    Article  Google Scholar 

  11. Zhang, Y., Lo, Y. H., Wong, W. S., & Shu, F. (2016). Protocol sequences for the multiple-packet reception channel without feedback. IEEE Transaction on Communication, 64(4), 1687–1698.

    Article  Google Scholar 

  12. Salaun, L., Chen, C. S., Chen, Y. & Wong, W. S. (2016). Constant delivery delay protocol sequences for the collision channel without feedback. In Proceedings of international symposium on wireless personal multimedia communication, Shenzhen, China.

  13. Nguyen, Q. A., Györfi, L., & Massey, J. L. (1992). Constructions of binary constant-weight cyclic codes and cyclically permutable codes. IEEE Transactions on Information Theory, 38(3), 940–949.

    Article  MathSciNet  MATH  Google Scholar 

  14. Györfi, L., & Vajda, I. (1993). Construction of protocol sequences for multiple-access collision channel without feedback. IEEE Transactions on Information Theory, 39(5), 1762–1765.

    Article  MATH  Google Scholar 

  15. Bitan, S., & Etzion, T. (1995). Constructions for optimal constant weight cyclically permutable codes and difference families. IEEE Transactions on Information Theory, 41(1), 77–87.

    Article  MathSciNet  MATH  Google Scholar 

  16. Yang, G. C., & Kwong, W. C. (1995). Performance analysis of optical CDMA with prime codes. IEEE Electron Letters, 31(7), 569–570.

    Article  Google Scholar 

  17. Yang, G. C., & Kwong, W. C. (2002). Prime codes with applications to CDMA optical and wireless networks. Norwood, MA: Artech House.

    Google Scholar 

  18. Shum, K. W., Wong, W. S., Sung, C. W., & Chen, C. S. (2009). Design and construction of protocol sequences: Shift invariance and user irrepressibility. In Proceedings of IEEE international symposium on information theory, Seoul, Korea (pp. 1368–1372).

  19. Shum, K. W., & Wong, W. S. (2010). Construction and applications of CRT sequences. IEEE Transactions on Information Theory, 56(11), 5780–5795.

    Article  MathSciNet  MATH  Google Scholar 

  20. Shum, K. W., Zhang, Y., & Wong, W. S. (2010). User-irrepressible sequences. In Proceedings of conference on SETA, Paris (pp. 88–101).

  21. Levenshtein, V. I., & Tonchev, V. D. (2005). Optimal conflict-avoiding codes for three active users. In: Proceedings of IEEE international symposium on information theory, Adelaide (pp. 535–537).

  22. Fu, H.-L., Lin, Y.-H., & Mishima, M. (2010). Optimal conflict-avoiding codes of even length and weight 3. IEEE Transactions on Information Theory, 56(11), 5747–5756.

    Article  MathSciNet  MATH  Google Scholar 

  23. Shum, K. W., Wong, W. S., & Chen, C. S. (2010). A general upper bound on the size of constant-weight conflict-avoiding codes. IEEE Transactions on Information Theory, 56(7), 3265–3276.

    Article  MathSciNet  MATH  Google Scholar 

  24. Lo, Y.-H., Fu, H.-L., & Lin, Y.-H. (2015). Weighted maximum matchings and optimal equi-difference conflict-avoiding codes. Designs, Codes and Cryptography, 76(2), 361–372.

    Article  MathSciNet  MATH  Google Scholar 

  25. Lin, Y., Mishima, M., & Jimbo, M. (2016). Optimal equi-difference conflict-avoiding codes of weight four. Designs, Codes and Cryptography, 78(3), 747–776.

    Article  MathSciNet  MATH  Google Scholar 

  26. Chung, F. R. K., Salehi, J. A., & Wei, V. K. (1989). Optimal optical orthogonal codes: Design, analysis, and applications. IEEE Transactions on Information Theory, 35(3), 595–604.

    Article  MathSciNet  MATH  Google Scholar 

  27. Wang, J., & Yin, J. (2010). Two-dimensional optical orthogonal codes and semicyclic group divisible designs. IEEE Transactions on Information Theory, 56(5), 2177–2187.

    Article  MathSciNet  MATH  Google Scholar 

  28. Feng, T., Wang, L., Wang, X., & Zhao, Y. (2016). Optimal two-dimensional optical orthogonal codes with the Best cross-correlation constraint. Journal of Combinatorial Designs, 25, 349–380.

    Article  MathSciNet  MATH  Google Scholar 

  29. Chlamtac, I., & Faragó, A. (1994). Making transmission schedules immune to topology changes in multihop packet radio networks. IEEE/ACM Transactions on Networking, 2(1), 23–29.

    Article  Google Scholar 

  30. Chu, W., Colbourn, C. J., & Syrotiuk, V. R. (2006). The effects of synchronization on topology-transparent scheduling. Wireless Networks, 12(6), 681–690.

    Article  Google Scholar 

  31. Chu, W., Colbourn, C. J., & Syrotiuk, V. R. (2006). Slot synchronized topology-transparent scheduling for sensor networks. Computer Communications, 29(4), 421–428.

    Article  Google Scholar 

  32. Liu, Y., Li, V. O. K., Leung, K.-C., & Zhang, L. (2014). Topology-transparent scheduling in mobile ad hoc networks with multiple packet reception capability. IEEE Transactions on Wireless Communications, 13(11), 5940–5953.

    Article  Google Scholar 

  33. Colbourn, C. J., Dinitz, J. H., & Stinson, D. R. (1999). Applications of combinatorial designs to communications, cryptography, and networking. In J. D. Lamb & D. A. Preece (Eds.) Surveys in combinatorics, ser. Lecture Note Series 267 (pp. 37–100). London: London Math. Soc.

  34. Hui, Y. N. (1984). Multiple accessing for the collision channel without feedback. IEEE Journal on Selected Areas in Communications, 2(4), 575–582.

    Article  Google Scholar 

  35. Zhang, Y., Shum, K. W., & Wong, W. S. (2011). Complete irrepressible sequences for the asynchronous collision channel without feedback. IEEE Transactions on Vehicular Technology, 60(4), 1859–1866.

    Article  Google Scholar 

  36. Ireland, K., & Rosen, M. (1990). A classical introduction to modern number theory. New York: Springer.

    Book  MATH  Google Scholar 

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Acknowledgements

The authors would like to express their gratitude to the anonymous referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China under Grant No. 61301107 and 11601454, the open research fund of National Mobile Communications Research Laboratory, Southeast University, under Grant No. 2017D09, and the Natural Science Foundation of Fujian Province of China under Grant No. 2016J05021.

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Authors and Affiliations

  1. School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing, China

    Yijin Zhang

  2. National Mobile Communications Research Laboratory, Southeast University, Nanjing, China

    Yijin Zhang

  3. School of Mathematical Sciences, Xiamen University, Xiamen, China

    Yuan-Hsun Lo

  4. Institute of Network Coding, The Chinese University of Hong Kong, Shatin, Hong Kong

    Kenneth W. Shum

  5. Department of Information Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong

    Wing Shing Wong

Authors
  1. Yijin Zhang
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  2. Yuan-Hsun Lo
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  3. Kenneth W. Shum
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  4. Wing Shing Wong
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Corresponding author

Correspondence to Yuan-Hsun Lo.

Additional information

The material in this paper was presented in part at Globecom 2014 Workshop on ULTRA, Austin, USA, Dec. 2014.

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Zhang, Y., Lo, YH., Shum, K.W. et al. New CRT sequence sets for a collision channel without feedback. Wireless Netw 25, 1697–1709 (2019). https://doi.org/10.1007/s11276-017-1623-x

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  • DOI: https://doi.org/10.1007/s11276-017-1623-x

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