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Develops a linear link between convolutional encoder states and syndrome former states, implying improved code analysis.
A linear correspondence is developed between the states of a rate- <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k/n</tex> convolutional encoder <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</tex> and the states of a corresponding syndrome former <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H^T</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> is an encoder of the code dual to the code generated by <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</tex> . This correspondence is used to find an expression for the number of all-zero paths of length <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">τ</tex> in the code trellis; the answer depends only on the constraint lengths of the dual code. A partial answer to the resynchronization problem also falls out of this development.
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G. David Forney (1973) studied this question.
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