  Two-dimensional constrained coding is a problem that is much more difficult
than its one-dimensional counterpart. Indeed, in two dimensions, obtaining the
answers to very natural questions becomes uncomputable. In particular, it is
undecidable to determine if it is possible to fill the infinite plane with
symbols in such a way that no forbidden pattern appears. Also, even when we
know that such an infinite plane exists, it is uncomputable to determine the
maximal rate at which payload data can be embedded into the selection of a
valid infinite plane. Recently, Nakamura et al. presented a technique that
efficiently performs the construction of a matrix of symbols that embeds
payload data. Their technique is efficient in the sense that the construction
takes time that is proportional to the area of the constructed matrix. Their
technique is based on the offline elaboration of a collection of tiles, which
is then used for the matrix construction. The collection-elaboration step is
time consuming and it might even never terminate nor succeed. In this work, we
extend their technique by generalizing their notion of tile. Our technique has
the potential to achieve much higher data-embedding rates.
