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Structural analysis of convolutional codes via dual codes

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A linear correspondence is developed between the states of a rate-k/nconvolutional encoderGand the states of a corresponding syndrome formerH^T, whereHis an encoder of the code dual to the code generated byG. This correspondence is used to find an expression for the number of all-zero paths of lengthtauin 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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Information Theory, IEEE Transactions on  (Volume:19 ,  Issue: 4 )