Strongly Conflict-Avoiding Codes

Abstract

Strongly conflict-avoiding codes are used in the asynchronous multiple-access collision channel without feedback. The number of codewords in a strongly conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, an upper bound on the size of strongly conflictavoiding codes is proved. In addition, we provide an improved upper bound if the codes are all equi-difference. This bound is further shown to be tight asymptotically.

Strongly Conflict-Avoiding Codes with Weight Three

“…Furthermore, the bound is shown to be sharp for some case such as length n 4; 20 ðmod 24Þ. However, Zhang et al [18] introduced a recursion method to construct an SCACð2n; wÞ from a CACðn; wÞ by doubling all elements in each codeword of the CACðn; wÞ. They established the following relationship between SCACs and CACs.…”

“…In 2011, Zhang et al [18] consider a more general scenario, in which the collision channel is asynchronous, i.e., all users do not know the slot boundaries of the channel. Strongly conflict-avoiding codes are used to a slot-asynchronous multiple-access collision channel without feedback to guarantee the non-blocking property.…”

“…In 2011, Zhang et al [18] introduced strongly conflict avoiding codes and gave a general upper bound on the size of SCACðn; wÞ. Especially, Uðn; wÞ ¼ 0 for n w and Uðn; wÞ ¼ 1 for w n 2w 2 [18,Theorem 2].…”

“…Especially, Uðn; wÞ ¼ 0 for n w and Uðn; wÞ ¼ 1 for w n 2w 2 [18,Theorem 2]. So we need only to consider the case n !…”

“…Theorem 22[18] If there exists a CAC ðn; wÞ with M codewords, then there exists an SCAC ð2n; wÞ with M codewords. Z. Yu, J. Wang According to Theorem 22 and the existence of CAC with length n and weight three, we obtain the lower bound on the size of strongly conflict-avoiding codes of length 2n and weight three.Lemma 23 Uð2n; 3Þ !…”