On weight enumerators and MacWilliams identity for convolutional codes

Summary, in English

Convolutional codes are defined to be equivalent if their code symbols differ only in how they are ordered and two generator matrices are defined to be weakly equivalent (WE) if they encode equivalent convolutional codes. It is shown that tailbiting convolutional codes encoded by WE minimal-basic generator matrices have the same spectra. Shearer and McEliece showed that MacWilliams identity does not hold for convolutional codes. However, for the spectra of truncated convolutional codes and their duals, MacWilliams identity clearly holds. It is shown that the dual of a truncated convolutional code is not a truncation of a convolutional code but its reversal is. Finally, a recursion for the spectra of truncated convolutional codes is given and the spectral components are related to those for the corresponding dual codes.

• Author: Irina Bocharova; Florian Hug; Rolf Johannesson; Boris Kudryashov
• Department/s: Department of Electrical and Information Technology
• Publishing year: 2010
• Language: English
• Publication/Series: [Host publication title missing]
• Links: http://dx.doi.org/10.1109/ITA.2010.5454120
• Document type: Conference paper
• Topic: Electrical Engineering, Electronic Engineering, Information Engineering
• Conference name: Information Theory and Applications Workshop (ITA), 2010
• Conference date: 2010-01-31 - 2010-02-05
• Conference place: San Diego, CA, United States
• Status: Published
• Research group: Information Theory