The capacity of finite Abelian group codes over symmetric memoryless channels
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2010
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| Online Access: | http://hdl.handle.net/1721.1/51996 |
| _version_ | 1826194010873528320 |
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| author | Como, Giacomo Fagnani, Fabio |
| author2 | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems |
| author_facet | Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Como, Giacomo Fagnani, Fabio |
| author_sort | Como, Giacomo |
| collection | MIT |
| description | 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. |
| first_indexed | 2024-09-23T09:49:08Z |
| format | Article |
| id | mit-1721.1/51996 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T09:49:08Z |
| publishDate | 2010 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/519962022-09-30T17:01:09Z The capacity of finite Abelian group codes over symmetric memoryless channels Como, Giacomo Fagnani, Fabio Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Como, Giacomo Como, Giacomo 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. 2010-03-03T14:26:40Z 2010-03-03T14:26:40Z 2009-04 2008-06 Article http://purl.org/eprint/type/JournalArticle 0018-9448 http://hdl.handle.net/1721.1/51996 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 en_US http://dx.doi.org/10.1109/TIT.2009.2015992 IEEE Transactions on Information Theory 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. application/pdf Institute of Electrical and Electronics Engineers IEEE |
| spellingShingle | Como, Giacomo Fagnani, Fabio The capacity of finite Abelian group codes over symmetric memoryless channels |
| title | The capacity of finite Abelian group codes over symmetric memoryless channels |
| title_full | The capacity of finite Abelian group codes over symmetric memoryless channels |
| title_fullStr | The capacity of finite Abelian group codes over symmetric memoryless channels |
| title_full_unstemmed | The capacity of finite Abelian group codes over symmetric memoryless channels |
| title_short | The capacity of finite Abelian group codes over symmetric memoryless channels |
| title_sort | capacity of finite abelian group codes over symmetric memoryless channels |
| url | http://hdl.handle.net/1721.1/51996 |
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