This paper presents a new approach to perform detection over frequency non-selective Rayleigh fading channels, via first-order Markov chains. We analyze the performance of the proposed algorithms considering various schemes, including iterative detection schemes. In particular, we show that the particular choice of the encoder influences the bit error rate (BER) performance. In order to limit the complexity of the multiple trellis techniques. We show that the complexity can be significantly reduced without affecting the performance.