On the Existence of Retransmission Permutation Arrays

We investigate retransmission permutation arrays (RPAs) that are motivated by applications in overlapping channel transmissions. An RPA is an $n\times n$ array in which each row is a permutation of $1,\mathrm{.}\mathrm{.}\mathrm{.},n$, and for $1\leq i\leq n$,all$n$symbolsoccurineach$i\times\lceil\frac{n}{i}\rceil$ rectangle in specified corners of the array. The array has types 1, 2, 3 and 4 if the stated property holds in the top left, top right, bottom left and bottom right corners, respectively. It is called latin if it is a latin square. We show that for all positive integers $n$, there exists a type-$1,2,3,4$ $\text{RPA}(n)$ and a type-1,2 latin $\text{RPA}(n)$.