Using Bivariate Generating Functions to Count the Number of Balanced Runlength-Limited Words
Filip Palunčić, Bodhaswar T Maharaj · 2017
A simple and general method is presented for enumerating the number of balanced (zero-disparity) runlength-limited words based on bivariate generating functions and the symbolic methods of analytic combinatorics. This procedure scales well with increasing word length, allowing for exact enumerations for very large word lengths. As a result, it serves as a precise benchmark against which to evaluate the performance, in terms of code rate, of balanced runlength-limited coding schemes.