While the field of one-dimensional constrained codes is mature, with
theoretical as well as practical aspects of code- and decoder-design being
well-established, such a theoretical treatment of its two-dimensional (2D)
counterpart is still unavailable. Research has been conducted on a few
exemplar 2D constraints, e.g., the hard triangle model, run-length limited
constraints on the square lattice, and 2D checkerboard constraints.
Excluding these results, 2D constrained systems remain largely
uncharacterized mathematically, with only loose bounds of capacities
present. In this paper we present a lozenge constraint on a regular
triangular lattice and derive Shannon noiseless capacity bounds. To estimate
capacity of lozenge tiling we make use of the bijection between the counting
of lozenge tiling and the counting of boxed plane partitions.
Amorphous Metal Oxide Bilayers to Avoid Sneak‐Path Currents for High‐Density Resistive Memory Arrays
