Variations on a Theme by Schalkwijk and Kailath
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05361503(1).pdf
Description
Main article
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329.79 KB
Format
Adobe PDF
Checksum (MD5)
30a2f7788846e52f05c535da30b478e9
Author(s)
Gallager, Robert G.
Nakiboglu, Baris
Date Issued
December 2009
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers
Citation
Gallager, R.G., and B. Nakiboglu. “Variations on a Theme by Schalkwijk and Kailath.” Information Theory, IEEE Transactions on 56.1 (2010): 6-17.
Version
Final published version
Abstract
Schalkwijk and Kailath (1966) developed a class of block codes for Gaussian channels with ideal feedback for which the probability of decoding error decreases as a second-order exponent in block length for rates below capacity. This well-known but surprising result is explained and simply derived here in terms of a result by Elias (1956) concerning the minimum mean-square distortion achievable in transmitting a single Gaussian random variable over multiple uses of the same Gaussian channel. A simple modification of the Schalkwijk-Kailath scheme is then shown to have an error probability that decreases with an exponential order which is linearly increasing with block length. In the infinite bandwidth limit, this scheme produces zero error probability using bounded expected energy at all rates below capacity. A lower bound on error probability for the finite bandwidth case is then derived in which the error probability decreases with an exponential order which is linearly increasing in block length at the same rate as the upper bound.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Massachusetts Institute of Technology. Research Laboratory of Electronics
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
https://doi.org/10.1109/TIT.2009.2034896
