Multichannel Conflict-Avoiding Codes of Weights Three and Four

Conflict-avoiding codes (CACs) were introduced by Levenshtein as a single-channel transmission scheme for a multiple-access collision channel without feedback. When the number of simultaneously active source nodes is less than or equal to the weight of a CAC, it is able to provide a hard guarantee that each active source node transmits at least one packet successfully within a fixed time duration, no matter what the relative time offsets between the source nodes are. In this article, we extend CACs to multichannel CACs for providing such a hard guarantee over multiple orthogonal channels. Upper bounds on the number of codewords for multichannel CACs of weights three and four are derived, and constructions that are optimal with respect to these bounds are presented.

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

[2]  R. C. Bose,et al.  Orthogonal Arrays of Strength two and three , 1952 .

[3]  Jehoshua Bruck,et al.  Codes for Asymmetric Limited-Magnitude Errors With Application to Multilevel Flash Memories , 2010, IEEE Transactions on Information Theory.

[4]  N. J. A. Sloane,et al.  The On-Line Encyclopedia of Integer Sequences , 2003, Electron. J. Comb..

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

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

[7]  Yiling Lin,et al.  Optimal equi-difference conflict-avoiding codes of weight four , 2016, Des. Codes Cryptogr..

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

[9]  Duan-Shin Lee,et al.  Asynchronous Grant-Free Uplink Transmissions in Multichannel Wireless Networks With Heterogeneous QoS Guarantees , 2019, IEEE/ACM Transactions on Networking.

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

[11]  Guu-chang Yang,et al.  Multiple-wavelength optical orthogonal codes under prime-sequence permutations for optical CDMA , 2005, IEEE Transactions on Communications.

[12]  Gennian Ge,et al.  On (g, 4;1)-difference matrices , 2005, Discret. Math..

[13]  A. Selvarajan,et al.  Two-dimensional optical orthogonal codes for fiber-optic CDMA networks , 2005, Journal of Lightwave Technology.

[14]  Jennifer Seberry,et al.  Generalized Bhaskar Rao Designs with Block Size 3 over Finite Abelian Groups , 2007, Graphs Comb..

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

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

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

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

[19]  Torleiv Kløve,et al.  Systematic, Single Limited Magnitude Error Correcting Codes for Flash Memories , 2011, IEEE Transactions on Information Theory.

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

[21]  Tsonka Stefanova Baicheva,et al.  Optimal conflict-avoiding codes for 3, 4 and 5 active users , 2017, Probl. Inf. Transm..

[22]  Eric A. rtOa,et al.  Packet Switching Satellites ' , 2005 .

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

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

[25]  Tsonka Stefanova Baicheva,et al.  Classification of optimal conflict-avoiding codes of weights 6 and 7 , 2017, Electron. Notes Discret. Math..

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

[27]  Koji Momihara,et al.  A new series of optimal tight conflict-avoiding codes of weight 3 , 2017, Discret. Math..

[28]  Wenping Ma,et al.  New optimal constructions of conflict-avoiding codes of odd length and weight 3 , 2014, Des. Codes Cryptogr..

[29]  Hung-Lin Fu,et al.  Weighted maximum matchings and optimal equi-difference conflict-avoiding codes , 2015, Des. Codes Cryptogr..

[30]  Fang Liu,et al.  Sequence-Based Unicast in Wireless Sensor Networks , 2020, IEEE Transactions on Communications.

[31]  Anthony B. Evans.  On orthogonal orthomorphisms of cyclic and non-abelian groups , 2002, Discret. Math..