This paper presents a theoretical probability distribution model for peak-to-average power ratio (PAPR) in the digital sub-carrier multiplexing (DSCM) system, which has not previously been proposed in the literature. To reduce PAPR, an interleaved discrete Fourier transform spread DSCM (I-DFT-S-DSCM) scheme is proposed, which introduces reversible correlations between subcarriers. To investigate the effectiveness of the proposed schemes, a 64-GBaud 16 quadrature amplitude modulation (16-QAM) DSCM system with 4, 8, and 16 sub-carriers was constructed. In the digital domain, the results demonstrate that the proposed theoretical PAPR probability distribution model exhibits mean squared errors (MSE) below 10-5 for the observed and model-predicted complementary cumulative distribution functions (CCDF) in both DSCM and I-DFT-S-DSCM schemes. Regarding PAPR reduction, the I-DFT-S-DSCM scheme demonstrated a reduction in PAPR of up to 1.44 dB compared to the conventional DSCM scheme. To further investigate the impact of PAPR on the bit error rate (BER) performance of the DSCM system, the I-DFT-S-DSCM scheme is implemented with 8 subcarriers transmitted over a 100-km standard single-mode fiber (SSMF). A comparative analysis with DSCM indicates that I-DFT-S-DSCM achieves a PAPR reduction of approximately 1.1 dB and improves receiver sensitivity by approximately 0.7 dB at a 7% hard-decision forward error correction (HD-FEC) threshold, in 100-km single-mode fiber SSMF transmissions.