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Non-orthogonal space-time block (STB) code structures used to be optimised considering a maximum-likelihood detection, but depending on the modulation order and/or the antenna number, the prohibitive complexity of such a receiver makes it infeasible in practice. Suboptimal low-complexity receiver structures like linear detectors can be applied instead, yielding degradation of performance compared with the predictions. When a forward error correction (FEC) code is used upstream of the STB code, an iterative receiver consisting of a FEC decoder and an interference canceller (IC) co-operating according to the turbo equalisation principle, can achieve near-optimal performance. This study aims to define the construction of full-rate full-diversity linear dispersion codes with reduced peak-to-average power ratio (PAPR), taking into account the serial concatenation with a FEC at the transmitter and a minimum mean square error (MMSE) turbo equaliser at the receiver. Optimisation criteria are mutual information maximisation, symbol error rate minimisation at the MMSE-IC output, full-diversity thanks to the threaded algebraic space time concept and PAPR minimisation. Explicit constructions are given and the resulting code efficiency is analysed through comparison with equivalent perfect STB codes.