On topological entropies of the subshifts associated with the stream version of asymmetric binary systems

Abstract

The stream version of asymmetric binary systems (ABS) invented by Duda is an entropy coder for information sources with a finite alphabet. It has the state parameter l of a nonnegative integer and the probability parameter p with 0 < p < 1. First we observe that the edge shift X_G associated with the stream version of ABS has the topological entropy h(X_G) = log 2. Then we define the edge shift X_H associated with output blocks from the stream version of ABS, and show that h(X_H) = h(X_G), which implies that X_G and X_H are finitely equivalent. The encoding and decoding algorithms for the stream version of ABS establish a bijection between X_G and X_H. We consider the case where p = 1/β with the golden mean β = (1 + √5)/2. Eventually we show that X_G and X_H are conjugate for l = 7, and that they are almost conjugate for l = 10.