MacWilliams identities for terminated convolutional codes
Shearer and McEliece showed that there is no MacWilliams identity for the free distance spectra of orthogonal linear convolutional codes. We show that on the other hand there does exist a MacWilliams identity between the generating functions of the weight distributions per unit time of a linear conv...
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| Format: | Article |
| Language: | en_US |
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Institute of Electrical and Electronics Engineers (IEEE)
2012
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| Online Access: | http://hdl.handle.net/1721.1/73077 |
| _version_ | 1826214355655458816 |
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| author | Forney, G. David, Jr. |
| author2 | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science |
| author_facet | Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Forney, G. David, Jr. |
| author_sort | Forney, G. David, Jr. |
| collection | MIT |
| description | Shearer and McEliece showed that there is no MacWilliams identity for the free distance spectra of orthogonal linear convolutional codes. We show that on the other hand there does exist a MacWilliams identity between the generating functions of the weight distributions per unit time of a linear convolutional code C and its orthogonal code C[superscript ⊥], and that this distribution is as useful as the free distance spectrum for estimating code performance. These observations are similar to those made recently by Bocharova et al.; however, we focus on terminating by tail-biting rather than by truncation. |
| first_indexed | 2024-09-23T16:04:05Z |
| format | Article |
| id | mit-1721.1/73077 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T16:04:05Z |
| publishDate | 2012 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/730772022-10-02T06:05:12Z MacWilliams identities for terminated convolutional codes Forney, G. David, Jr. Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Forney, G. David, Jr. Shearer and McEliece showed that there is no MacWilliams identity for the free distance spectra of orthogonal linear convolutional codes. We show that on the other hand there does exist a MacWilliams identity between the generating functions of the weight distributions per unit time of a linear convolutional code C and its orthogonal code C[superscript ⊥], and that this distribution is as useful as the free distance spectrum for estimating code performance. These observations are similar to those made recently by Bocharova et al.; however, we focus on terminating by tail-biting rather than by truncation. 2012-09-20T17:52:43Z 2012-09-20T17:52:43Z 2010-06 Article http://purl.org/eprint/type/ConferencePaper 978-1-4244-7891-0 978-1-4244-7890-3 http://hdl.handle.net/1721.1/73077 Forney, G. David. “MacWilliams Identities for Terminated Convolutional Codes.” 2010 IEEE International Symposium on Information Theory Proceedings (ISIT). 1105–1109. © Copyright 2010 IEEE en_US http://dx.doi.org/10.1109/ISIT.2010.5513699 2010 IEEE International Symposium on Information Theory Proceedings (ISIT) 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) IEEE |
| spellingShingle | Forney, G. David, Jr. MacWilliams identities for terminated convolutional codes |
| title | MacWilliams identities for terminated convolutional codes |
| title_full | MacWilliams identities for terminated convolutional codes |
| title_fullStr | MacWilliams identities for terminated convolutional codes |
| title_full_unstemmed | MacWilliams identities for terminated convolutional codes |
| title_short | MacWilliams identities for terminated convolutional codes |
| title_sort | macwilliams identities for terminated convolutional codes |
| url | http://hdl.handle.net/1721.1/73077 |
| work_keys_str_mv | AT forneygdavidjr macwilliamsidentitiesforterminatedconvolutionalcodes |