On the number of encoder states for capacity approaching d = 1 codes

The number of encoder states is a key measure of complexity of a finite-state constrained code. In this paper, we derive analytically the relationship between the number of encoder states and the size of capacity approaching d = 1 codes. By defining the number of encoder states as (generalized) Fibonacci numbers, we obtain the optimum encoder states, which maximize the size of the designed code with minimum number of states, for any desired codeword length