This paper proposes likelihood function generation of complexity-reduced Maximum Likelihood Detection with QR Decomposition and M-algorithm (QRM-MLD) suitable for soft-decision Turbo decoding and investigates the throughput performance using QRM-MLD with the proposed likelihood function in multipath Rayleigh fading channels for Orthogonal Frequency and Code Division Multiplexing (OFCDM) multiple-input multiple-output (MIMO) multiplexing. Simulation results show that by using the proposed likelihood function generation scheme for soft-decision Turbo decoding following QRM-MLD in 4-by-4 MIMO multiplexing, the required average received signal energy per bit-to-noise power spectrum density ratio (Eb/N0) at the average block error rate (BLER) of 10-2 at a 1-Gbps data rate is significantly reduced compared to that using hard-decision decoding in OFCDM access with 16 QAM modulation, the coding rate of 8/9, and 8-code multiplexing with a spreading factor of 8 assuming a 100-MHz bandwidth. Furthermore, we show that by employing QRM-MLD associated with soft-decision Turbo decoding for 4-by-4 MIMO multiplexing, the throughput values of 500 Mbps and 1 Gbps are achieved at the average received Eb/N0 of approximately 4.5 and 9.3 dB by QPSK with the coding rate of R = 8/9 and 16QAM with R = 8/9, respectively, for OFCDM access assuming a 100-MHz bandwidth in a twelve-path Rayleigh fading channel.