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

We show that the state complexity profile of a convolutional code C is the same as that of the reciprocal of the dual code of C in case that minimal encoders for both codes are used. Then, we propose an optimum permutation for any given (n, n - 1) binary convolutional code that will yield an equivalent code with the lowest state complexity. With this permutation, we are able to find many (n, n - 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.