Insertion rate and optimization of redundancy of constrained systems with unconstrained positions

It was recently shown that the code rate of a simple coding scheme is better than a previously established maxentropic bound for the Wijngaarden-Immink reversed modulation and error control scheme(W-I coding scheme). This paper analyzes code rates of coding schemes for a given insertion rate of the W-I coding scheme using finite state transition diagrams. A new coding scheme is proposed and a new bound for the code rate of the W-I coding scheme is derived. It is proved that the new bound is better than the maxentropic bound when the insertion rate is 1/2.