When the requirements of internet of things (IoT) and machine-type communication (MTC) are considered, the 5G technology needs to support high spectral efficiency and massive connectivity of users/devices, and the demand for low latency, short packet duration, low power, high mobility and diverse service types. In this paper, first a new multiple access technique belonging to the class of non-orthogonal multiple access (NOMA) based on multi-code signaling (MCS) is proposed for the uplink data transmission mode in severe multi-path fading channels in order to handle the key challenges of 5G technology. This new technique combines the index modulation in code domain with channel division multiple access (ChDMA) on which a novel receiver architecture is structured at significantly reduced complexity. Second, an efficient message passing algorithm (MPA), which realizes iterative maximum a posteriori probability (MAP) detection with linear complexity in the number of interfering users, is proposed. The novel feature of the proposed MPA stems from the use of Ungerboeck factorization, where the whitening filter is avoided before MAP detection. The joint task of equalization and multi-user detection (MUD) is fulfilled via the introduced Ungerboeck type sum-product algorithm (SPA) framework. This architecture for general NOMA transmission, operating on the resultant Ungerboeck type factor-graph (FG) with bidirectional feedback, achieves dramatic complexity reduction (compared to conventional FG based algorithms).