Turbo decoding of concatenated channel coding and trellis shaping for peak power controlled single-carrier systems

Trellis shaping (TS) has found its application in the peak power control of band-limited single-carrier signals. Our recent work has demonstrated that a well-designed TS can control the symbol transitions such that the output signal has almost constant envelope, which significantly alleviates the linearity requirement of power amplifiers. Compared to transmission without constellation shaping, however, the TS involves signal constellation expansion exclusively for peak power control. Therefore, unlike trellis coded modulation (TCM) that increases the minimum Euclidean distances (MED), the TS decreases the MED, thus incurring the increase in signal-to-noise power ratio (SNR) required for achieving a certain error rate. In this letter, in order to overcome this drawback, we propose a serial concatenation of coding and shaping together with an effective decoding algorithm that utilizes the memory effect (i.e., error correcting capability) of the shaped symbols. The achievable performance of the proposed system is analyzed in terms of the average mutual information. The simulation results demonstrate that the iterative decoding of the proposed concatenated system with outer convolutional codes and inner trellis shaping offers a significant performance gain.