A joint channel coding and probabilistic shaping (PS) scheme is proposed and experimentally demonstrated in an intensity modulation and direct-detection optical discrete multi-tone (DMT) interconnection. The PS-32 quadrature amplitude modulation (PS-32QAM) is probabilistically reshaped from a 6-bit/symbol 64QAM signal based on polar-coded many-to-one (MTO) mapping, enabling a Gaussian-like symbol probability distribution without shaping or forward error correction redundancy. A bit-interleaved polar-coded modulation iterative decoding system based on joint QAM demapping and polar decoding is employed to retrieve the multi-labeled PS symbols. Experimental results indicate that the polar-coded PS-32QAM DMT signal achieves a 1.5-dB receiver power sensitivity improvement and a 2.71-dB fiber nonlinearity tolerance enhancement over 10-km standard single-mode fiber transmission.