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In this paper, we investigate the combination of error-correcting codes and a multicode scheme with constant amplitude transmission. This multicode scheme can be considered as a single parity check (SPC) coding scheme since a parity check bit is generated by a nonlinear operation at the transmitter side. In order to improve the overall performance by efficient utilization of these parity check bits, error-correcting codes are employed in the scheme. We analyze Hamming codes, Gallager's codes and zigzag codes, used in the precoder, respectively. It is obvious that the combination is equivalent to a compound encoder with serial concatenation. At the receiver side, efficient decoding of this compound code is the key to improvement of performance. According to its coding structure, an iterative decoding scheme for the proposed system is given, based on a message passing algorithm. The performance of the coding schemes are simulated and the results show that combinations of error-correcting codes and this multicode scheme contribute to greatly improved performance.