This paper considers uplink interleave division multiple access (IDMA), of which crucial requirement is the proper operability at a very low signal-to-interference-plus-noise power ratio (SINR) range. The primary objectives of this paper are threefold: (1) to demonstrate the achievability of near-capacity performance of bit interleaved coded modulation with iterative detection (BICM-ID) using very low rate single parity check and irregular repetition (SPC-IrR) codes at a very low SINR range, and hence the technique is effective in achieving excellent performance when it is applied for IDMA, (2) to propose a very simple multiuser detection (MUD) technique for the SPC-IrR BICM-ID IDMA which does not incur heavy per-iteration computational burden, and (3) to analyze the impacts of power allocation on the convergence property of MUD as well as on the rate region, by using the extrinsic information transfer (EXIT) chart. The SPC-IrR code parameters are optimized by using the EXIT-constrained binary switching algorithm (EBSA) at a very low SINR range. Simulation results show that the proposed technique can achieve excellent near-capacity performance with the bit error rate (BER) curves exhibiting very sharp threshold, which significantly influences the convergence property of MUD. Furthermore, this paper presents results of the rate region analysis of multiple access channel (MAC) in the cases of equal and unequal power allocation, as well as of a counterpart technique. The results of the MAC rate region analysis show that our proposed technique outperforms the counterpart technique.