2-D Wavelet Codes for Correcting 2-D Burst Errors
The synthesis bank of a two-channel two-variable filter bank over the finite field is used to design a two-dimensional (2-D) code, and the corresponding analysis bank is used to generate the syndrome of the code. First, we studied the encoder of half-rate TDWCs and show that these linear codes are lattice cyclic. It is proven that any 2-D lattice-cyclic code can also be generated by a 2-D wavelet transform. Second, we introduced a methodology to design TDWCs over binary erasure channels. These codes have simple and efficient maximum likelihood (ML) decoding for burst erasures. We showed that half-rate TDWCs of dimensions N1 × N2 can recover burst erasures of size up to N1 × N2/2 and N1/2 × N2 using our proposed simple decoding technique. Finally, we presented examples of TDWCs that satisfy the Reiger bound with equality, i.e., they are capable of correcting any burst of size N1N2/2.