The Principle of Re-Encoding Parity Check Symbols and Its Application to the Correction of Two-Dimensional Clusters of Errors

A novel construction method is presented for array codes correcting a single rectangular error cluster of size b₁ × b₂ or less. Encoding is done in such a way that parity check symbols calculated by rows resp. columns itselves are each a word of a one-dimensional code correcting a phased burst. These parity check symbols are not transmitted but can be calculated by the receiver. Corresponding decoding algorithms are given. A code is constructed with maximum size n₁ = b¹2^b2, n₂ = b₂2^b1 and r = 3b₁b₂ redundancy symbols which is close to the generalized Singleton bound r ≥ 2b₁b₂. Its encoding and decoding complexity are low.