Sparse Code Multiple Access (SCMA), a Non-Orthogonal Multiple Access (NOMA) technique, is one of the auspicious candidates for fifth/sixth-generation (5G/6G) and beyond wireless communication systems. Due to the sparsity of SCMA, the Message Passing Algorithm (MPA) can be deployed at the receiver end to achieve near-optimal performance, even in Rayleigh fading channels. However, one of the main drawbacks of MPA is its high complexity. Interference Cancellation (IC) techniques are employed to reduce decoding complexity. These interference cancellation techniques decode one user in the presence of interference noise from the remaining users. Hybrid Interference Cancellation (HIC) with Log-domain MPA (HIC-Log MPA) is an efficient method to mitigate complexity, but the decoder’s strategy depends on each user’s power levels. Practically, each user may have specific Quality of Service (QoS) requirements, which may include ensuring a certain Bit Error Rate (BER) for that user. Since BER depends on Signal-to-Interference Noise Ratio (SINR), optimizing Power Allocation (PA) becomes of paramount importance when employing an HIC-Log MPA decoder in SCMA systems. Effective PA optimization ensures that QoS requirements are met and helps prevent error propagation. In this paper, we propose a power allocation strategy for an uplink SCMA system. The strategy aims to achieve a target BER to ensure QoS for all users, utilizing a low-cost and computationally efficient decoder.