Picture codes and deciphering delay

A set X of pictures over an alphabet Σ is a code if any picture over Σ is tilable in at most one way with pictures in X. The codicity problem is in general undecidable. Recently, the prefix picture codes were introduced as a decidable subclass of codes that generalize the prefix string codes. In the string theory, the finite deciphering delay sets are some interesting codes which coincide with the prefix codes when the delay is equal to 0. An analogous notion is introduced for the picture codes and it is proved that the codes with deciphering delay k form a decidable class of picture codes which includes interesting examples and special cases.