On the design of variable-rate optimal convolutional encoders for turbo codes

Recently, we proposed a new design technique to construct high-rate convolutional codes based on a structure formed by a block encoder and a simpler convolutional encoder (Graell i Amat, A. et al., IEEE Commun.. Lett., vol.5, no.11, p.453-5, 2001). The search technique was based on the optimization of the output weight enumerating function of the code. We now prove that every (n,n-1) convolutional code can be reduced to this structure. Following this result and suitably modifying our earlier search algorithm, we have been able to obtain the best (n, n-1) convolutional encoders to be used in the design of turbo codes. In this case, the search is aimed at the optimization of the input-output weight enumerating function of the encoders. We also derive an inverse puncturing method that can be applied to these high-rate convolutional codes to obtain a sequence of the (almost) best convolutional encoders. With such a method, a whole family of good encoders with different rates is obtained using the same encoder-decoder, thus permitting a great versatility that can be exploited in practical implementations.