New Recursive Convolutional GF(2N) Encoders for Parallel Turbo-TCM Schemes

In this paper, parallel turbo phase shift keying – trellis coded modulation (Turbo PSK-TCM) schemes are designed using recursive convolutional encoders over Galois field GF(2^N). These encoders are designed using the nonlinear left-circulate (LCIRC) function. The LCIRC function performs a bit left circulation over the representation word. An optimum 1-delay GF(2^N) recursive convolutional encoder scheme using LCIRC (RC-LCIRC) is proposed for PSK-TCM schemes. The minimum Euclidian distance is estimated for these PSK-TCM schemes and it is shown that these structures offer the maximum coding gains. However, the RC-LCIRC encoders are less complex than the corresponding binary encoders. The optimum RC-LCIRC encoder is used as component encoder of a parallel turbo PSK-TCM transmission scheme, using the iterative multilevel log-MAP algorithm in the receiver. The bit error rate (BER) is estimated by simulation for the proposed Turbo PSK-TCM transmissions over an additive white Gaussian noise (AWGN) channel, and the results are similar to the conventional Turbo-TCM schemes.