Parallel constrained coding with application to two-dimensional constraints

A (one-dimensional) constraint is defined as the set of all finite words that axe generated by a given labeled finite directed graph G. Examples of constraints include the (d, k)-runlength-limited (RLL) constraints and the symmetric runlength (SRLL) constraints. In the latter, the runlengths of 0´s, as well as the runlengths of 1´s, are between d and k, except that the first and last runlengths may be shorter than d. A commonly-used coding model for constraints is that of a finite-state encoder at a fixed rate p:q. In this work, we explore the possibility of obtaining simple coding schemes by encoding several input streams simultaneously, i.e., in parallel. The coding model is still a finite-state encoder at a fixed rate p:q. Yet, an input p-block is mapped into q output symbols, each belonging now to a different track; the sequence generated along each track belongs to a given constraint S. Decoding is carried out by reading q tracks at a time and reconstructing the respective input p-block. If the resulting encoder is block decodable, then such a reconstruction requires only the knowledge of the current symbol in each track.