##### Department of Mathematics,

University of California San Diego

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### Applications

## Roxana Smarandache

#### San Diego State University

## Large Convolutional Codes with Maximal or near-Maximal Distance

##### Abstract:

In comparison to the literature on linear block codes there existonly relatively few algebraic constructions ofconvolutional codes having some good designed distance. There areeven fewer algebraic decoding algorithms which are capable ofexploiting the algebraic structure of the code.Convolutional codes are typically decoded via the Viterbialgorithm which has the advantage that soft information can beprocessed. This algorithm has however the disadvantage that it istoo complex for codes with large degree or large memory or whenthe block length is large. The algorithm is also not practicalfor convolutional codes defined over large alphabets. There aresome alternative sub-optimal algorithms such as sequentialdecoding and feedback decoding. All these algorithms do not in generalexploit the algebraic structure of the convolutional code.In this talk some good classes of algebraic convolutional codeswill be introduced. These codes are particularly suited for applicationswhere large alphabets are involved. The free distance of these codesis the maximal possible distance a convolutional code of a certainrate and degree can have. It is shown that these codes can decode amaximum number of errors per time interval when compared with otherconvolutional codes of the same rate and degree.These codes have also a maximum or near maximum distance profile.A code has a maximum distance profile if and only if the dual code hasthis property.Professor Smarchande will give a TUTORIAL at 12.30 in APM 7218 on communications

Host: Bill Helton

### April 15, 2003

### 5:00 PM

### AP&M 7321

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