A Simple Converse of Burnashev's Reliability Function
Name
Berlin-2006-A Simple Converse of.pdf
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Author(s)
Berlin, Peter
Nakiboglu, Baris
Rimoldi, Bixio
Telatar, Emre
Date Issued
June 2009
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers
Citation
Berlin, P. et al. “A Simple Converse of Burnashev's Reliability Function.” Information Theory, IEEE Transactions on 55.7 (2009): 3074-3080. © 2009 Institute of Electrical and Electronics Engineers
Version
Final published version
Abstract
In a remarkable paper published in 1976, Burnashev determined the reliability function of variable-length block codes over discrete memoryless channels (DMCs) with feedback. Subsequently, an alternative achievability proof was obtained by Yamamoto and Itoh via a particularly simple and instructive scheme. Their idea is to alternate between a communication and a confirmation phase until the receiver detects the codeword used by the sender to acknowledge that the message is correct. We provide a converse that parallels the Yamamoto-Itoh achievability construction. Besides being simpler than the original, the proposed converse suggests that a communication and a confirmation phase are implicit in any scheme for which the probability of error decreases with the largest possible exponent. The proposed converse also makes it intuitively clear why the terms that appear in Burnashev's exponent are necessary.
Subjects
variable-length communication
reliability function
feedback
discrete memoryless channels (DMCs)
Burnashev's error exponent
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
http://dx.doi.org/10.1109/TIT.2009.2021322
