Consider the MIMO detection background. While the hard-decision Sphere Decoder has been widely and recently considered as the most promising near-optimal detector, this perspective might fall down during the soft-decision extension through a List Sphere Decoder (LSD). Due to the finiteness of the LSD list output-that does not necessarily allow for generating explicitly the Log-Likelihood Ratios (LLRs), even through a max-log approximation-the issue of how to set the missing reliabilities has

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... n addressed. This paper presents existing works concerning the main trend. In particular, it consists in setting the LLR to a pre-defined value, this operation being commonly referred as LLR Clipping. We discuss this choice that has a significant impact on the system performance, by providing a brief state of the art of the existing solutions. In addition in the presented work, a novel solution lies in the multi-level bit mapping. Despite of its simplicity, it allows for low distortion approximated LLR computation. By simulation, the superiority of our method over the existing solutions, is shown.