Criss-Cross Deletion Correcting Codes

This paper studies the problem of constructing codes correcting deletions in arrays. Under this model, it is assumed that an n × n array can experience deletions of rows and columns. These deletion errors are referred to as (t
_r
, t
_c
)-criss-cross deletions if t
_r
rows and t
_c
columns are deleted, while a code correcting these deletion patterns is called a (t
_r
, t
_c
)-criss-cross deletion correcting code. The definitions for criss-cross insertions are similar.Similar to the one-dimensional case, it is first shown that the problems of correcting criss-cross deletions and criss-cross insertions are equivalent. Then, we mostly investigate the case of (1, 1)criss-cross deletions. An asymptotic upper bound on the cardinality of (1, 1)-criss-cross deletion correcting codes is shown which assures that the asymptotic redundancy is at least 2n-2+2 log n bits. Finally, a code construction with an explicit decoding algorithm is presented. The redundancy of the construction is away from the lower bound by at most 2 log n+ 9 + 2 log e bits.