Rate k/(k+1) punctured convolutional encoders

G.D. Forney (1970, 1975) defined a minimal encoder as a polynomial matrix G such that G generates the code and G has the least constraint length among all generators for the code. Any convolutional code can be generated by a minimal encoder. High-rate k(k+1) punctured convolutional codes were introduced to simplify Viterbi decoding. An ordinary convolutional encoder G can be obtained from any punctured encoder. A punctured encoder is minimal if the corresponding ordinary encoder G is minimal and the punctured and ordinary encoders have the same constraint length. It is shown that any rate k/(k+1), noncatastrophic, antipodal punctured encoder is a minimal encoder.