On the structure of rate1/nconvolutional codes
L.R. Bahl, F. Jelinek · IEEE Transactions on Information Theory · 1972
We show what choice there is in assigning output digits to transitions of a binary rate1/ncode 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\upsiloneach binary sequence of length2j(1 \leq j \leq \upsilon - 1)is associated with exactly2^{\upsilon -j -1}distinct pathsjbranches 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 rate1/nconvolutional codes and use our results to determine the length of the largest input sequence that can conceivably result in an output whose weight is