Kraft–McMillan inequality Free semigroup Integer matrix 1. Introduction Let S be a semigroup and let X be a subset of S. Then X is called a code if for any integers m,n≥1 and any elements x1,…,xm,y1,…,yn∈X the equationx1x2…xm=y1y2…yn implies thatm=nandxi=yifor1≤i≤...
The second part of the thesis touches on the Kraft-McMillan Inequality. Since the proof of this latter inequality uses limits, we cannot immediately analyse its equality cases. The paper will therefore study the equality cases of this theorem and demonstrate that these equality cases have similar ...
In this short paper, we shall provide a dynamical systems' proof of the famous Kraft-McMillan inequality and its converse. Kraft-McMillan inequality is a basic result in information theory which gives a necessary and sufficient condition for the lengths of the codewords of a code to be ...
We prove a version of the Kraft–McMillan inequality for free semigroups of upper-triangular integer matrices of any dimension.Juha HonkalaInformation and ComputationJuha Honkala. A Kraft-McMillan inequality for free semigroups of upper-triangular matrices. Information and Computation, 239:216-221, ...