Markov capacity for factor codes with an unambiguous symbol

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2023-11-07 DOI:10.1017/etds.2023.103

GUANGYUE HAN, BRIAN MARCUS, CHENGYU WU

引用次数: 0

Abstract

Abstract In this paper, we first give a necessary and sufficient condition for a factor code with an unambiguous symbol to admit a subshift of finite type restricted to which it is one-to-one and onto. We then give a necessary and sufficient condition for the standard factor code on a spoke graph to admit a subshift of finite type restricted to which it is finite-to-one and onto. We also conjecture that for such a code, the finite-to-one and onto property is equivalent to the existence of a stationary Markov chain that achieves the capacity of the corresponding deterministic channel.

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具有明确符号的因子码的马尔可夫容量

摘要本文首先给出了具有明确符号的因子码允许有限类型子位移的一个充要条件，该子位移是一对一和映上的。然后给出了辐图上标准因子码允许有限型子位移的充分必要条件，该子位移是有限到1且有限到上的。我们还推测，对于这样一个码，有限到一和上的性质等价于一个达到相应确定性信道容量的平稳马尔可夫链的存在。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.