Multiple Criss-Cross Insertion and Deletion Correcting Codes

This paper investigates the problem of correcting multiple criss-cross insertions and deletions in arrays. More precisely, we study the unique recovery of n x n arrays affected by t-criss-cross deletions defined as any combination of t(r) row and t(c) column deletions such that t(r)+t(c)=t for a given t . We show an equivalence between correcting t -criss-cross deletions and t -criss-cross insertions and show that a code correcting t -criss-cross insertions/deletions has redundancy at least t(n)+t logn-log(t!) . Then, we present an existential construction of a t -criss-cross insertion/deletion correcting code with redundancy bounded from above by tn+O(t(2)log(2)n) . The main ingredients of the presented code construction are systematic binary t -deletion correcting codes and Gabidulin codes. The first ingredient helps locating the indices of the inserted/deleted rows and columns, thus transforming the insertion/deletion-correction problem into a row/column erasure-correction problem which is then solved using the second ingredient.