## On the growth rate of convolutional codes

#### Reports in Informatics No. 172, May 1999, Department of
Informatics, University of Bergen, Norway.

#### Abstract

Let $\mathcal C$ be a rate $(n-r)/n$ convolutional code with canonical
parity-check matrix $\mathbf{H}(D)$, and let $w_0$ denote the minimum
average weight per edge over all nonzero cycles in the state diagram for
$\mathcal C$. The rate of growth per edge of the minimum distance between
two nonmerged codewords is given by the value of $w_0$. For any code
$\mathcal C$, we show how to obtain an upper bound on $w_0$ from the
columns of $\mathbf{H}(D)$.
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