Parallel turbo-TCM schemes using recursive convolutional GF(2N) encoders over frequency non-selective fading channel

In this paper, recursive convolutional encoders over Galois field GF(2^N) are used as constituent codes in a parallel turbo trellis coded modulation (turbo TCM) scheme. 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 phase shift keying - trellis-coded modulation (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. As advantage, the RC-LCIRC encoders are less complex than the corresponding binary encoders for a fixed encoding rate. The parallel turbo TCM transmission schemes with optimum RC-LCIRC encoder as component encoder are investigated using the iterative symbol-by-symbol log-MAP algorithm in the receiver. The considered modulations schemes are 8-PSK and 16-quadrature amplitude modulation (16-QAM). The bit error rate (BER) is estimated by simulation for the proposed turbo TCM transmissions over a frequency non-selective fading channel with additive white Gaussian noise (AWGN). The simulation results are similar to the conventional turbo TCM schemes.