Two-dimensional error correcting codes using finite-field wavelets

This paper introduces two-dimensional wavelet codes (TDWC's). First, we study the encoder of half-rate TDWC's. 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's over binary erasure channels. We show that the half-rate TDWC's of dimensions N-1 x N-2 can recover burst erasures of size up to N-1 x N-2/2 and N-1/2 x N-2, and N-2/2 x N-2. Finally, we present examples of TDWC's that satisfy the Reiger bound with equality (capable of correcting any burst of size N-1 N-2/2). Since these codes are lattice-cyclic, their erasure decoding can be simplified.