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The original turbo codes (TCs), presented in 1993 by Berrou et al., consist of the parallel concatenation of two rate-1/2 binary recursive systematic convolutional (RSC) codes. This paper explains how replacing rate-1/2 binary component codes by rate-m/(m+1) binary RSC codes can lead to better global performance. The encoding scheme can be designed so that decoding can be achieved closer to the theoretical limit, while showing better performance in the region of low error rates. These results are illustrated with some examples based on double-binary (m=2) 8-state and 16-state TCs, easily adaptable to a large range of data block sizes and coding rates. The double-binary 8-state code has already been adopted in several telecommunication standards.