On (n, n-1) convolutional codes with low trellis complexity

We show that the state complexity profile of a convolutional code is the same as that of the reciprocal of the dual code of in case that minimal encoders for both codes are used. Then, we propose an optimum permutation for any given ( 1) binary convolutional code that will yield an equivalent code with the lowest state complexity. With this permutation, we are able to find many ( 1) binary convolutional codes which are better than punctured convolutional codes of the same code rate and memory size by either lower decoding complexity or better weight spectra.