Continuity of Channel Parameters and Operations under Various DMC Topologies

Abstract

We study the continuity of many channel parameters and operations under various topologies on the space of equivalent discrete memoryless channels (DMC). We show that mutual information, channel capacity, Bhattacharyya parameter, probability of error of a fixed code, and optimal probability of error for a given code rate and blocklength, are continuous under various DMC topologies. We also show that channel operations such as sums, products, interpolations, and Arıkan-style transformations are continuous.

31 pages. Submitted to IEEE Trans. Inform. Theory and in part to ISIT2017

References in corpus (4)

• Polarization for arbitrary discrete memoryless channels
• Ergodic Theory Meets Polarization. I: An Ergodic Theory for Binary Operations
• Ergodic Theory Meets Polarization. II: A Foundation of Polarization Theory
• Continuity of Channel Parameters and Operations under Various DMC Topologies

Cited by in corpus (2)

• Continuity of Channel Parameters and Operations under Various DMC Topologies
• Complexity and Second Moment of the Mathematical Theory of Communication