Data center networks (DCNs) require a low-cost, low-power optical transceiver to handle increased traffic from generative artificial intelligence, video streaming services, and more. Improving the required signal-to-noise ratio (RSNR) by digital signal processing such as forward error correction (FEC) mitigates the requirements for electrical and optical components. The optical transceivers in DCNs exploit a low-complexity soft-decision (SD) FEC, consisting of short block-length linear error-correcting codes and a low-complexity SD decoder (SDD), such as Chase decoding and ordered statistics decoding. The low-complexity SDD efficiently approaches a maximum likelihood decoding (MLD). However, the decoding performance of MLD is limited by its finite block length. In this paper, we describe the details of our proposed channel-polarized multilevel coding with iterative decoding (CP-MLC-ID). The proposed CP-MLC-ID improves the decoding performance by extending the codeword length to weakly and indirectly connect codewords via bypassed bits. The 19.5%-OH CP-MLC-ID using 128-bit extended Bose-Chaudhuri-Hocquenghem (eBCH) and KP4 codes outperforms the concatenated eBCH and KP4 codes with a net coding gain of 0.25 and 0.40 dB for the same and double the number of SDDs, respectively. We also investigate the dependency of the decoding performance on the size of a bit interleaver. The performance degradation of CP-MLC-ID using an 8-bit interleaver is about 0.1 dB compared to using the large-bit interleaver. Our results indicate that even a weak connection by exclusive-OR between codewords improves the decoding performance, compared to simple concatenated codes in the DCNs.