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

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...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 59; no. 12; pp. 8027 - 8056
Main Author: Dalai, Marco
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.12.2013
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Capacity planning
Classical-quantum channels
Codes
Coding, codes
Context
cutoff rate
Errors
Exact sciences and technology
Information theory
Information, signal and communications theory
Lovász theta function
Probabilistic logic
Probability distribution
quantum Chernoff bound
Reliability
reliability function
Rényi divergence
Signal and communications theory
sphere packing bound
Telecommunications and information theory
Upper bound
Vectors
sphere packing bound
Lower bound
quantum Chernoff bound
Error probability
reliability function
Lovász theta function
Rényi divergence
Quantum channel
Coding
cutoff rate
Reliability
Renyi theory
Classical-quantum channels
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary: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.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2013.2283794