On (n,n-1) Punctured Convolutional Codes and Their Trellis Modules

It is known that an (n,n-1) non catastrophic antipodal punctured convolutional encoder of memory m is minimal. That is, the corresponding code cannot be produced by an encoder of smaller memory size. In this letter it is shown that the trellis module of a code produced by an (n,n-1) non catastrophic punctured convolutional encoder is optimum, if and only if the encoder is antipodal.