Two-dimensional error correcting codes using finite-field wavelets

This paper introduces two-dimensional wavelet codes (TDWC). First, we study the encoder of half-rate TDWC. We show that these linear codes are lattice-cyclic. We prove that any two-dimensional lattice-cyclic code can also be generated by a two-dimensional wavelet transform. Second, we introduce a methodology to design TDWC over binary erasure channels. We show that the half-rate TDWC of dimensions N/sub 1/ /spl times/ N/sub 2/ can recover burst erasures of size up to N/sub 1/ /spl times/ N/sub 2//2 and N/sub 1//2 /spl times/ N/sub 2/, and N/sub 2//2 /spl times/ N/sub 2/. Finally, we present examples of TDWC that satisfy the Reiger bound with equality (capable of correcting any burst of size (N/sub 1/N/sub 2/)/2). Since these codes are lattice-cyclic, their erasure decoding can be simplified.