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- W2171528946 abstract "We show what choice there is in assigning output digits to transitions of a binary rate <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1/n</tex> code trellis so that the latter will correspond to a convolutional code. We then prove that in any rate <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>frac{1}{2}</tex> noncatastrophic code of constraint length <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>upsilon</tex> each binary sequence of length <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2j</tex> <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>(1 leq j leq upsilon - 1)</tex> is associated with exactly <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>2^{upsilon -j -1}</tex> distinct paths <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>j</tex> 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 <tex xmlns:mml=http://www.w3.org/1998/Math/MathML xmlns:xlink=http://www.w3.org/1999/xlink>1/n</tex> 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" @default.
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- W2171528946 date "1972-01-01" @default.
- W2171528946 modified "2023-09-23" @default.
- W2171528946 title "On the structure of rate<tex>1/n</tex>convolutional codes" @default.
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- W2171528946 doi "https://doi.org/10.1109/tit.1972.1054749" @default.
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