Comment on "An upper bound on run-length coding entropy"

In the above letter, the authors prove that their equation (11) has one and only one solution in the interval 0 < x < 1 when 1 < R < (M + 1)/2 and, in the interval x > 1 when R > (M + 1)/2. It is my aim to provide an alternative proof to Theorem 1 and to show that a stronger result can be obtained with the help of Descartes’ rule of signs [1] and symmetry considerations. The equation under consideration is the following :