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On the structure of rate 1/n convolutional codes

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2 Author(s)

We show what choice there is in assigning output digits to transitions of a binary rate 1/n code trellis so that the latter will correspond to a convolutional code. We then prove that in any rate frac{1}{2} noncatastrophic code of constraint length \upsilon each binary sequence of length 2j (1 \leq j \leq \upsilon - 1) is associated with exactly 2^{\upsilon -j -1} distinct paths j branches long. As a consequence of the above properties nondegenerate codes with branch complementarity are fully determined by the topological relationship of the trellis transitions associated with output pairs 00. Finally, we derive a new upper bound on free distance of rate 1/n convolutional codes and use our results to determine the length of the largest input sequence that can conceivably result in an output whose weight is

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IEEE Transactions on Information Theory  (Volume:18 ,  Issue: 1 )