New CRT sequence sets for a collision channel without feedback
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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.
KeywordsCollision channel without feedback Protocol sequences User-irrepressible sequences CRT sequences Conflict-avoiding codes
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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