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Maximum-likelihood detection (MLD) can achieve optimum performance for the vertical Bell laboratories layered space-time (V-BLAST) architecture. However, due to its exponentially high computational complexity, several near-optimal detection algorithms, including some parallel detection (PD) ones with low complexity and high stability, have been proposed instead for practical systems. Nevertheless, the existing PD algorithms have a common drawback in equally handling all the branches obtained via exhaustive interference cancellation (EIC) till reaching the final minimum Euclidean distance (MED) decision. In this paper, a simplified PD algorithm, i.e., a generalized parallel interference cancellation (GPIC) algorithm has been developed by means of early termination of the inferior parallel branches. The algorithm is abbreviated as simplified GPIC (SGPIC) algorithm. Numerical analysis indicates that SGPIC algorithm can achieve the near-optimal performance with much lower complexity in comparison with the existing PD algorithms, especially for the cases of high order constellations. Thus, the SGPIC algorithm makes the parallel detection more feasible in practical systems with limited parallel processing elements.