On the use of splitting vectors with zero components for constrained encoder design

The state-splitting algorithm is a method for designing an encoder for a constrained system of the type prevalent in digital recording system technology. Traditionally, the starting point of the state-splitting algorithm involves finding a “splitting vector”, a vector with positive integer components whose component sum is an upper bound on the number of states of the encoder to be designed. We give a tutorial on the use of splitting vectors in which some of the components are allowed to be zero. This leads to an encoder with fewer states in some cases. The MATLAB code is given for generating such splitting vectors