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On locally invertible rate-1/n convolutional encoders

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4 Author(s)
D. L. Bitzer ; Dept. of Comput. Sci., North Carolina State Univ., Raleigh, NC, USA ; A. Dholakia ; H. Koorapaty ; M. A. Vouk

A locally invertible convolutional encoder has a local inverse defined as a full rank w×w matrix that specifies a one-to-one mapping between equal-length blocks of information and encoded bits. In this correspondence, it is shown that a rate-1/n convolutional encoder is nondegenerate and noncatastrophic if and only if it is locally invertible. Local invertibility is used to obtain upper and lower bounds on the number of consecutive zero-weight branches in a convolutional codeword. Further, existence of a local inverse can be used as an alternate test for noncatastrophicity instead of the usual approach involving computation of the greatest common divisor of n polynomials

Published in:

IEEE Transactions on Information Theory  (Volume:44 ,  Issue: 1 )