Criss-Cross Deletion Correcting Codes
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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 correction code. The definitions for criss-cross insertions are similar. Similar to the one-dimensional case, it is first shown that when t_r=t_c 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 correction codes is shown which assures that the asymptotic redundancy is at least 2n-1+2log 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+8+2log e bits.
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