Uniform Latin square interleaving for correcting two-dimensional burst errors

A Latin square is widely used as an interleaving algorithm with an error-correcting code to correct burst errors in storage and communication systems. In a storage system, there are two types of burst errors; successive errors occurring on one track, i.e. a 1-dimensional burst error, and 1-dimensional burst errors occurring over successive tracks, i.e. a 2-dimensional burst error. The 1-dimensional burst error is usually caused by surface contamination or thermal asperity in the read head and the 2-dimensional burst error is usually caused by defects in the recording medium. We introduce here a new class of Latin square, a uniform Latin square, that can improve 2-dimensional error-correction capability compared with that of the conventional Latin squares.