The Error Probability of Generalized Perfect Codes via the Meta-Converse
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Vazquez-Vilar, Gonzalo
Guillen i Fabregas, Albert https://orcid.org/0000-0003-2795-1124
Verdu, Sergio
Abstract
We introduce a definition of perfect and quasiperfect codes for discrete symmetric channels based on the packing and covering properties of generalized spheres whose shape is tilted using an auxiliary probability measure. This notion generalizes previous definitions of perfect and quasiperfect codes and encompasses maximum distance separable codes. The error probability of these codes, whenever they exist, is shown to coincide with the estimate provided by the metaconverse lower bound. We illustrate how the proposed definition naturally extends to cover almost-lossless source-channel coding and lossy compression.
Description
Keywords
Shannon theory, perfect codes, quasi-perfect codes, maximum likelihood decoding, finite blocklength analysis, meta-converse, hypothesis testing, channel coding, joint source-channel coding, rate distortion theory
Journal Title
IEEE TRANSACTIONS ON INFORMATION THEORY
Conference Name
Journal ISSN
0018-9448
1557-9654
1557-9654
Volume Title
65
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
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Rights
All rights reserved
Sponsorship
European Research Council (725411)
ERC