On Locally Invertible Rate-1/n Convolutional Encoders

A locally invertible convolutional encoder has a local inverse defined as a full rank w/spl times/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.