Constructions for retransmission permutation arrays

Li, Liu, Tan, Viswanathan, and Yang [3] 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 retransmission 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.