LOZENGE TILING CONSTRAINED CODES

While the field of one-dimensional constrained codesis mature, with theoretical as well as practical aspects of codeanddecoder-design being well-established, such a theoreticaltreatment of its two-dimensional (2D) counterpart is still unavailable.Research has been conducted on a few exemplar2D constraints, e.g., the hard triangle model, run-length limitedconstraints on the square lattice, and 2D checkerboardconstraints. Excluding these results, 2D constrained systemsremain largely uncharacterized mathematically, with only loosebounds of capacities present. In this paper we present a lozengeconstraint on a regular triangular lattice and derive Shannonnoiseless capacity bounds. To estimate capacity of lozenge tilingwe make use of the bijection between the counting of lozengetiling and the counting of boxed plane partitions