Capacity of constrained sequence codes modelled by two-dimensional finite state machines with nearest-neighbour connections

Constrained sequence codes are widely used to help meet constraints imposed by digital storage and communication systems. This paper presents a straightforward approach to evaluate the capacity of constrained sequence codes that are modelled by a two-dimensional finite state machine (FSM) with nearest-neighbour connections. Starting with the equivalent one-dimensional constraint, we show how the eigenvalues of the resulting connection matrix increase as the size of the second dimension is increased. Further, we demonstrate how this knowledge can be applied to code design, in that with a given capacity in mind, the code designer is able to determine the set of two-dimensional constraints that will meet this capacity.