Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels
Typical minimum distances and error exponents are analyzed on the 8-PSK Gaussian channel for two capacity-achieving code ensembles with different algebraic structure. It is proved that the typical group code over the cyclic group of order eight achieves both the Gilbert-Varshamov bound and the expur...
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers
2011
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| Online Access: | http://hdl.handle.net/1721.1/67495 |
| _version_ | 1811096802908176384 |
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| author | Como, Giacomo |
| 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 |
| author_sort | Como, Giacomo |
| collection | MIT |
| description | Typical minimum distances and error exponents are analyzed on the 8-PSK Gaussian channel for two capacity-achieving code ensembles with different algebraic structure. It is proved that the typical group code over the cyclic group of order eight achieves both the Gilbert-Varshamov bound and the expurgated error exponent. On the other hand, the typical binary-coset codes (under any labeling) is shown to be bounded away both from the Gilbert-Varshamov bound (at any rate) and the expurgated exponent (at low rates). The reason for this phenomenon is shown to rely on the symmetry structure of the 8-PSK constellation, which is known to match the cyclic group of order eight, but not the direct product of three copies of the binary group. The presented results indicate that designing group codes matching the symmetry of the channel guarantees better typical-code performance than designing codes whose algebraic structure does not match the channel. This contrasts the well-known fact that the average binary-coset code achieves both the capacity and the random-coding error exponent of any discrete memoryless channel. |
| first_indexed | 2024-09-23T16:49:15Z |
| format | Article |
| id | mit-1721.1/67495 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:49:15Z |
| publishDate | 2011 |
| publisher | Institute of Electrical and Electronics Engineers |
| record_format | dspace |
| spelling | mit-1721.1/674952022-09-29T21:42:46Z Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels Como, Giacomo Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Como, Giacomo Como, Giacomo Typical minimum distances and error exponents are analyzed on the 8-PSK Gaussian channel for two capacity-achieving code ensembles with different algebraic structure. It is proved that the typical group code over the cyclic group of order eight achieves both the Gilbert-Varshamov bound and the expurgated error exponent. On the other hand, the typical binary-coset codes (under any labeling) is shown to be bounded away both from the Gilbert-Varshamov bound (at any rate) and the expurgated exponent (at low rates). The reason for this phenomenon is shown to rely on the symmetry structure of the 8-PSK constellation, which is known to match the cyclic group of order eight, but not the direct product of three copies of the binary group. The presented results indicate that designing group codes matching the symmetry of the channel guarantees better typical-code performance than designing codes whose algebraic structure does not match the channel. This contrasts the well-known fact that the average binary-coset code achieves both the capacity and the random-coding error exponent of any discrete memoryless channel. 2011-12-09T19:20:42Z 2011-12-09T19:20:42Z 2010-08 2009-10 Article http://purl.org/eprint/type/JournalArticle 0018-9448 http://hdl.handle.net/1721.1/67495 Como, G. “Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels.” Information Theory, IEEE Transactions on 56.9 (2010): 4321-4334.© 2010 IEEE. en_US http://dx.doi.org/10.1109/tit.2010.2054330 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 Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels |
| title | Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels |
| title_full | Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels |
| title_fullStr | Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels |
| title_full_unstemmed | Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels |
| title_short | Group Codes Outperform Binary-Coset Codes on Nonbinary Symmetric Memoryless Channels |
| title_sort | group codes outperform binary coset codes on nonbinary symmetric memoryless channels |
| url | http://hdl.handle.net/1721.1/67495 |
| work_keys_str_mv | AT comogiacomo groupcodesoutperformbinarycosetcodesonnonbinarysymmetricmemorylesschannels |