The Boltzmann sequence-structure channel

Abram Manager; Daisuke Kihara; Wojciech Szpankowski

doi:10.1109/isit.2016.7541300

The Boltzmann sequence-structure channel

Abstract

We rigorously study a channel that maps binary sequences to self-avoiding walks in the two-dimensional grid, inspired by a model of protein statistics. This channel, which we also call the Boltzmann sequence-structure channel, is characterized by a Boltzmann/Gibbs distribution with a free parameter corresponding to temperature. In our previous work, we verified experimentally that the channel capacity has a phase transition for small temperature and decays to zero for high temperature. In this paper, we make some progress towards explaining these phenomena. We first upper bound the conditional entropy between the input sequence and the output which exhibits a phase transition with respect to temperature. Then we derive a lower bound on the conditional entropy for some specific set of parameters. This lower bound allows us to conclude that the mutual information tends to zero for high temperature.

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Category:: Conference activity
Type:: publikacja w wydawnictwie zbiorowym recenzowanym (także w materiałach konferencyjnych)
Title of issue:: 2016 IEEE International Symposium on Information Theory strony 1 - 5
ISSN:: 2157-8117
Language:: Chinese
Publication year:: 2016
Bibliographic description:: Manager A., Kihara D., Szpankowski W.: The Boltzmann sequence-structure channel// 2016 IEEE International Symposium on Information Theory/ Barcelona: Information Theory (ISIT), 2016 IEEE International Symposium on, 2016, s.1-5
DOI:: Digital Object Identifier (open in new tab) 10.1109/isit.2016.7541300
Verified by:: Gdańsk University of Technology