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 N₁ × N₂ can recover burst erasures of size up to N₁ × N₂/2 and N₁/2 × N₂, and N₂/2 × N₂. Finally, we present examples of TDWC that satisfy the Reiger bound with equality (capable of correcting any burst of size (N₁N₂)/2). Since these codes are lattice-cyclic, their erasure decoding can be simplified.