Variable-length state splitting with applications to average runlength-constrained (ARC) codes

A new class of constrained systems average runlength constraints (ARCs), is defined by requiring that the sum of n consecutive run lengths be bounded above by a linear function of n. In particular, the running average runlength of every sequence in the system is bounded above by a constant. A general result is given on the capacity of ARC systems. The state splitting algorithm is then improved for variable-length graphs. This is then applied to obtain high, fixed-rate codes from the free binary source to ARC systems. As an example, a rate 1/2, (d,k)=