Abstract
Li et al. (Retransmission ≠ repeat: simple retransmission permutation can resolve overlapping channel collisions, 2009) introduced a technique for resolving overlapping channel transmissions that used an interesting new type of combinatorial structure. In connection with this problem, they provided an example of a 4 × 4 array having certain desirable properties. We define a class of combinatorial structures, which we term retrans mission permutation arrays, that generalise the example that Li et al. provided. We show that these arrays exist for all possible orders. We also define some extensions having additional properties, for which we provide some partial results.
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References
Bailey R.A., Cameron P., Connelly R.: Sudoku, gerechte designs, resolutions, affine space, spreads, reguli, and Hamming codes. Am. Math. Mon. 115(5), 383–404 (2008)
Colbourn C.J., Heinrich K.E.: Conflict-free access to parallel memories. J. Parallel Distrib. Comput. 14, 193–200 (1992)
Erickson D.L., Colbourn C.J.: Conflict-free access to rectangular subarrays. Congr. Numer. 90, 239–253 (1992)
Li L.E., Liu J., Tan K., Viswanathan H., Yang Y.R.: Retransmission ≠ repeat: simple retransmission permutation can resolve overlapping channel collisions. Eighth ACM Workshop on Hot Topics in Networks (HotNets-VIII), 2009.
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Dinitz, J.H., Paterson, M.B., Stinson, D.R. et al. Constructions for retransmission permutation arrays. Des. Codes Cryptogr. 65, 325–351 (2012). https://doi.org/10.1007/s10623-012-9684-4
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DOI: https://doi.org/10.1007/s10623-012-9684-4