In this manuscript, we propose an optimization framework to maximize the energy efficiency of the BSC-enabled cooperative NOMA system under imperfect successive interference cancellation (SIC) decoding at the receiver. Specifically, the energy efficiency of the system is maximized by optimizing the transmit power of the source, power allocation coefficients (PAC) of NOMA users, and power of the relay node. A low-complexity energy-efficient alternating optimization framework is introduced which simultaneously optimizes the transmit power of the source, PAC, and power of the relay node by considering the quality of service (QoS), power budget, and cooperation constraints under the imperfect SIC decoding. Subsequently, a joint channel coding framework is provided to enhance the performance of far user which has no direct communication link with the base station (BS) and has bad channel conditions. In the destination node, the far user data is jointly decoded using a Sum-product algorithm (SPA) based joint iterative decoder realized by jointly-designed Quasi-cyclic Low-density parity-check (QC-LDPC) codes obtained from cyclic balanced sampling plans excluding contiguous units (CBSEC). Simulation results evince that the proposed BSC-enabled cooperative NOMA system outperforms its counterpart by providing an efficient performance in terms of energy efficiency. Also, proposed jointly-designed QC-LDPC codes provide an excellent bit-error-rate (BER) performance by jointly decoding the far user data for considered BSC cooperative NOMA system with only a few decoding iterations under Rayleigh-fading transmission.