We propose a novel coded integrated passive sensing and communication (CIPSAC) system with orthogonal frequency division multiplexing (OFDM), where a multi-antenna base station (BS) passively senses the parameters of the targets and decodes the information bit sequences transmitted by a user. The transmitted signal is comprised of pilot and data OFDM symbols where the data symbols adopt cyclic redundancy check (CRC)-assisted channel codes to facilitate both the decoding and sensing procedures. In the proposed scheme, CRC not only enhances the reliability of communication but also provides guidance to the parameter sensing procedure at the BS. In particular, a novel iterative parameter sensing and channel decoding (IPSCD) algorithm is proposed, where the correctly decoded codewords that pass CRC are utilized for sensing to improve the parameter estimation accuracy, and in return, more accurate parameter estimates lead to a larger number of correctly decoded data symbols. Conventional sensing algorithms rely only on the received pilot signals, while we utilize both the data and pilot signals for sensing. We provide a detailed analysis of the optimal strategy, in which the wrongly decoded data packets are replaced by zero codewords. To further improve the performance, we introduce learning-based near-orthogonal superposition (NOS) codes, which exhibit superior error correction capability especially in the short block length regime. NOS codes are trained using a weighted loss function, where a hyper parameter is introduced to balance the sensing and the communication losses. Simulation results show the effectiveness of the proposed CIPSAC system and the IPSCD algorithm, where both the sensing and decoding performances are significantly improved with a few iterations. We also carry out extensive ablation studies for a comprehensive understanding of the proposed scheme.