The capacity of finite Abelian group codes over symmetric memoryless channels
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Como_Capacity-of-Finite.pdf
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435.39 KB
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Author(s)
Como, Giacomo
Fagnani, Fabio
Date Issued
April 2009
Journal
IEEE Transactions on Information Theory
Publisher
Institute of Electrical and Electronics Engineers
Citation
Como, G., and F. Fagnani. “The Capacity of Finite Abelian Group Codes Over Symmetric Memoryless Channels.” Information Theory, IEEE Transactions on 55.5 (2009): 2037-2054. © 2009 Institute of Electrical and Electronics Engineers
Version
Final published version
Abstract
The capacity of finite Abelian group codes over symmetric memoryless channels is determined. For certain important examples, such as m -PSK constellations over additive white Gaussian noise (AWGN) channels, with m a prime power, it is shown that this capacity coincides with the Shannon capacity; i.e., there is no loss in capacity using group codes. (This had previously been known for binary-linear codes used over binary-input output-symmetric memoryless channels.) On the other hand, a counterexample involving a three-dimensional geometrically uniform constellation is presented in which the use of Abelian group codes leads to a loss in capacity. The error exponent of the average group code is determined, and it is shown to be bounded away from the random-coding error exponent, at low rates, for finite Abelian groups not admitting Galois field structure.
MIT Department
Massachusetts Institute of Technology. Laboratory for Information and Decision Systems
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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.2009.2015992
