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We propose a generalized selection combining (GSC) scheme for binary signaling in which M diversity branches providing the largest magnitude of log-likelihood ratio (LLR) are selected and combined. The bit error probability provided by LLR-based GSC serves as a lower bound on the bit error probability provided by any GSC techniques. We also propose a suboptimal GSC based on a noncoherent envelope detection. We derive the bit error probability with LLR-based and envelope-based GSC techniques and examine their power gains over the conventional SNR-based GSC technique. We show that the bit error probability with maximum ratio combining or square-law combining of L branches is identical to that with LLR-based GSC of L/2 branches.