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A new Galois Field GF (2N) structure for designing Recursive Systematic Convolutional (RSC) encoders is presented in this paper. The proposed RSC encoders are used as components of a parallel-concatenated Turbo Trellis Coded Modulation (TTCM) scheme. The GF (2N) RSC encoders include a nonlinear function named left-circulate (LCIRC), which is performing a left circulation over the N bits representation word. A closed-form expression was found for the minimum Euclidian distance of rate (N 1) =N LCIRC-RSC encoders for (2N) -ary PSK-TCM, and its values show that these RSC-LCIRC encoders are optimum, having the same performances as the corresponding conventional binary encoders. However, the RSC-LCIRC encoders are less complex than the corresponding binary encoders for a given encoding rate.
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