Optimal strongly conflict-avoiding codes of even length and weight three

Strongly conflict-avoiding codes (SCACs) are employed in a slot-asynchronous multiple-access collision channel without feedback to guarantee that each active user can send at least one packet successfully in the worst case within a fixed period of time. By the assumption that all users are assigned distinct codewords, the number of codewords in an SCAC is equal to the number of potential users that can be supported. SCACs have different combinatorial structure compared with conflict-avoiding codes (CACs) due to additional collisions incurred by partially overlapped transmissions. In this paper, we establish upper bounds on the size of SCACs of even length and weight three. Furthermore, it is shown that some optimal CACs can be used to construct optimal SCACs of weight three.

[1]  Kenneth W. Shum,et al.  Shift-Invariant Protocol Sequences for the Collision Channel Without Feedback , 2009, IEEE Transactions on Information Theory.

[2]  Vladimir I. Levenshtein,et al.  Conflict-avoiding codes and cyclic triple systems , 2007, Probl. Inf. Transm..

[3]  Kenneth W. Shum,et al.  Optimal conflict-avoiding codes of odd length and weight three , 2014, Des. Codes Cryptogr..

[4]  Hung-Lin Fu,et al.  Optimal Conflict-Avoiding Codes of Even Length and Weight 3 , 2010, IEEE Transactions on Information Theory.

[5]  Kenneth W. Shum,et al.  Strongly Conflict-Avoiding Codes , 2011, SIAM J. Discret. Math..

[6]  Vladimir D. Tonchev,et al.  On Conflict-Avoiding Codes of Length $n=4m$ for Three Active Users , 2007, IEEE Transactions on Information Theory.

[7]  Kenneth W. Shum,et al.  A tight asymptotic bound on the size of constant-weight conflict-avoiding codes , 2010, Des. Codes Cryptogr..

[8]  Meinard Müller,et al.  Constant Weight Conflict-Avoiding Codes , 2007, SIAM J. Discret. Math..

[9]  Kenneth W. Shum,et al.  Completely Irrepressible Sequences for the Asynchronous Collision Channel Without Feedback , 2011, IEEE Transactions on Vehicular Technology.

[10]  Kenneth W. Shum,et al.  A General Upper Bound on the Size of Constant-Weight Conflict-Avoiding Codes , 2010, IEEE Transactions on Information Theory.

[11]  Kenneth W. Shum,et al.  Construction and Applications of CRT Sequences , 2010, IEEE Transactions on Information Theory.

[12]  Vladimir D. Tonchev,et al.  Optimal conflict-avoiding codes for three active users , 2005, Proceedings. International Symposium on Information Theory, 2005. ISIT 2005..

[13]  László Györfi,et al.  Constructions of binary constant-weight cyclic codes and cyclically permutable codes , 1992, IEEE Trans. Inf. Theory.

[14]  László Györfi,et al.  Constructions of protocol sequences for multiple access collision channel without feedback , 1993, IEEE Trans. Inf. Theory.

[15]  Koji Momihara,et al.  Necessary and sufficient conditions for tight equi-difference conflict-avoiding codes of weight three , 2007, Des. Codes Cryptogr..

[16]  Hung-Lin Fu,et al.  Optimal conflict-avoiding codes of length n ≡ 0 (mod 16) and weight 3 , 2009, Des. Codes Cryptogr..

[17]  Hung-Lin Fu,et al.  Optimal Tight Equi‐Difference Conflict‐Avoiding Codes of Length n = 2k ± 1 and Weight 3 , 2013 .

[18]  James L. Massey,et al.  The collision channel without feedback , 1985, IEEE Trans. Inf. Theory.

[19]  Yiling Lin,et al.  Optimal equi-difference conflict-avoiding codes of odd length and weight three , 2014, Finite Fields Their Appl..

[20]  W. S. Wong.  New Protocol Sequences for Random-Access Channels Without Feedback , 2007, IEEE Transactions on Information Theory.