This paper develops a new paradigm for the multi-input multi-output detection problem with bit interleaved coded modulation (MIMO-BICM). This new paradigm is based on a geometric method rather than the traditional interference cancellation or tree search. It describes in greater detail the soft-output detector called list exploration and exploitation (L2E), which builds a list of candidates from a geometrical interpretation of a given objective function. It then computes the log-likelihood ratios (LLRs) using the max-log approximation. A comparative study between L2E and a classical tree-based algorithm is carried out in both computational complexity and detection performance. This study highlights that although the framework is entirely different, the complexity and performance are comparable with the state of the art tree-based paradigm. Finally, the proposed algorithm is implemented on a field-programmable gate array (FPGA) device. Simulations carried out with Xilinx Vivado tools and measurements are provided to analyze the resource utilization, power consumption, and timing metrics. We further estimate these metrics for an application-specific integrated circuit (ASIC) implementation based on multiplicative factors from literature. This projection demonstrates that our implementation yields results of the same magnitude as the well-known detectors.