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 [1]. The search technique was based on the optimization of the output weight enumerating function of the code. Here, we prove that every (n, n − 1) convolutional code can be reduced to this structure. Following this result and suitably modifying the search algorithm in [1] 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 aiming at the optimization of the inputoutput 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.