Two-Dimensional Half-Rate Codes Using Two-Dimensional Finite-Field Filter Banks

This correspondence introduces two-dimensional (2-D) filter bank codes (TDFBCs). The synthesis bank of a two-channel two-dimensional filter bank over a finite field is used to design the 2-D code, and the corresponding analysis bank is used to generate the syndrome of the code. First, we study the encoder of half-rate TDFBCs 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 filter bank. Second, we introduce a methodology to design TDFBCs over binary erasure channels. These codes have a simple and efficient maximum-likelihood (ML) decoding algorithm for burst erasures. We show that half-rate TDFBCs of dimensions N₁ X N₂/ can recover burst erasures of size up to N₁ X N₂ /2 and N₁ /2 X N₂ using the proposed decoding technique. Finally, we present examples of TDFBCs that satisfy the Reiger bound with equality, i.e., they are capable of correcting any burst of size N₁ X N₂ /2 .