Symbol Insertion: A Low-Complexity Joint Peak Power Reduction and Forward Error Correction for Single-Carrier Systems

In this paper, we present a new modulation code, named symbol insertion (SI), that simultaneously achieves both peak-to-average power ratio (PAPR) reduction and forward error correction for pulse-shaped single-carrier systems in a low-complexity manner. Based on the fact that PAPR highly depends on the successive phase patterns of discrete complex symbols, the proposed code controls phase shifts by inserting a redundant symbol between consecutive information-bearing symbols. At the receiver, by viewing the inserted symbols as parities, we exploit them for error correction. We show that, when the SI is used as an inner code of serially concatenated codes, its error rate performance is close to those of conventional capacity-approaching codes. The proposed system thus becomes favorable if the amount of PAPR reduction is taken into account. Furthermore, the SI with a rotationally invariant insertion scheme can accommodate itself to noncoherent detection.