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The hard-square model is a two-dimensional (2-D) constrained system consisting of all binary arrays on a rectangular grid in which 1's are isolated both horizontally and vertically. This paper proposes algorithms to search for single-state and finite-state block codes with rectangular codewords that satisfy the hard-square constraint. Although the codeword size is small, single-state block codes with coding rates larger than 0.5 can be designed. Letting the 2-D constrained sequences have finite memory increases the achievable coding rate. A method for designing low-complexity encoders and decoders is also presented. When the codeword size increases, the coding rate asymptotically approaches the capacity but with rapidly increasing complexity of the encoder and decoder.
Date of Publication: Aug. 2005