Punctured turbo trellis code design for 8-PSK

In this paper, a new turbo trellis coded modulation (T-TCM) scheme is proposed for 8-PSK modulation. Belief propagation algorithm is used for T-TCM decoding. Bit and symbol interleaving techniques are considered for the T-TCM scheme and it is concluded that the symbol interleaved scheme provides better error performance. It is also shown by computer simulations that the distance distribution of the output symbol sequences for the two-weight inputs is improved when primitive feedback polynomials are selected for the constituent encoders instead of nonprimitive ones. Factors that determine performance at high signal to noise ratio are stated. If constituent encoders which maximize the output distances for two- and three-weight inputs are selected, those with maximum effective free distance with minimum multiplicity among them will provide the best error performance. From this issue, a new 8-state punctured T-TCM code for 8-PSK is designed and it is shown by computer simulations that it performs better especially at high SNR ratios with half decoding complexity, compared to the corresponding codes given in the literature.