Lower Bounds on the Probability of Error for Classical and Classical-Quantum Channels

Jump to other IT Society Websites:

Lower Bounds on the Probability of Error for Classical and Classical-Quantum Channels

Author(s):

Creation Date: Jul 06, 2014

Published In: Dec 2013

Paper Type: Journal Article

Book Title: IEEE Transactions on Information Theory

Abstract:

In this paper, lower bounds on error probability in coding for discrete classical and classical-quantum channels are studied. The contribution of the paper goes in two main directions: 1) extending classical bounds of Shannon to classical-quantum channels, and 2) proposing a new framework for lower bounding the probability of error of channels with a zero-error capacity in the low rate region. The relation between these two problems is revealed by showing that Lovász' bound on zero-error capacity emerges as a natural consequence of the sphere packing bound once we move to the more general context of classical-quantum channels. A variation of Lovász' bound is then derived to lower bound the probability of error in the low rate region by means of auxiliary channels. As a result of this study, connections between the Lovász theta function, the expurgated bound of Gallager, the cutoff rate of a classical channel, and the sphere packing bound for classical-quantum channels are established.

IEEE Explore link: http://dx.doi.org/10.1109/TIT.2013.2283794

Award(s) Received:

COVID-19 Updates

Read important changes and updates to the 2020 activities of the IEEE Information Theory Society due to the COVID-19 pandemic at:

https://www.itsoc.org/covid

 

Table of Contents

IEEE TechNav