In this paper, we propose bit-interleaved multiple access (BIMA) to enable Internet-of-Things (IoT) networks where a massive connection is required with limited resource blocks. First, by providing a true power allocation (PA) constraint for conventional NOMA with practical constraints, we demonstrate that it cannot support massive connections. To this end, we propose BIMA where there are no strict PA constraints, unlike conventional NOMA, thus allowing a high number of devices. We provide a comprehensive analytical framework for BIMA for all key performance indicators (KPIs) (i.e., ergodic capacity [EC], outage probability [OP], and bit error rate [BER]). We evaluate Jain's fairness index and proportional fairness index in terms of all KPIs. Based on the extensive computer simulations, we reveal that BIMA outperforms conventional NOMA significantly, with a performance gain of up to 20-30dB. This performance gain becomes greater when more devices are supported. BIMA provides a full diversity order and enables the implementation of an arbitrary number of devices and modulation orders, which is crucial for IoT networks in dense areas. BIMA guarantees a fairness system where none of the devices gets a severe performance and the sum-rate is shared in a fair manner among devices by guarantying QoS satisfaction. Finally, we provide an intense complexity and latency analysis and demonstrate that BIMA provides lower latency compared to conventional NOMA since it allows parallel computing at the receivers and no iterative operations are required. We show that BIMA reduces latency by up to 350\% for specific devices and 170\% on average.