Internet-of-Things (IoT) networks require massive connections in dense areas. Therefore, a resource efficient multiple access scheme seems inevitable to enable immense connectivity where multiple devices have to share the same resource block. Non-orthogonal multiple access (NOMA) has been considered as the strongest candidate in recent years. However, in this paper, by considering the practical implementation, we first provide a true power allocation (PA) constraint with finite alphabet inputs for conventional downlink NOMA and demonstrate that it cannot support massive connections in practical systems. To this end, we propose bit-interleaved multiple access (BIMA) scheme in downlink IoT networks. The proposed BIMA scheme implements bitwise multiaccess interleaving and deinterleaving at the transceiver ends and there are no strict PA constraints, unlike conventional NOMA, thus allowing a high number of devices in the same resource block. We provide a comprehensive analytical framework for BIMA by investigating all key performance indicators (KPIs) to present both information-theoretic (i.e., ergodic capacity [EC] and outage probability [OP]) and finite alphabet inputs (i.e., bit error rate [BER]) performance metrics with both instantaneous and statistical channel ordering. In addition, we define 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 20-30 dB in terms of KPIs in some scenarios. In other words, compared to conventional NOMA schemes, the same KPIs are met in BIMA with 20-30 dB less transmit power, which is quite promising for energy-limited use cases. Moreover, this performance gain becomes greater when more IoT devices are supported. BIMA provides a full diversity order for all IoT devices and enables the implementation of an arbitrary number of devices and modulation orders, which is crucial for IoT networks where a huge number of devices should be supported in a single resource block in dense areas. In addition to the overall performance gain, BIMA guarantees a fairness system where none of the devices gets a severely degraded performance and the sum-rate is shared in a fair manner among devices. It guarantees QoS satisfaction for all devices. Finally, we provide an intense complexity and latency analysis for BIMA and demonstrate that it provides lower latency compared to conventional NOMA receivers, since it allows parallel computation at the receivers and no iterative operations are required. We show that compared to conventional NOMA receivers, BIMA reduces latency by up to 350% for specific IoT devices and 170% on average.