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Selection diversity combining employed in conjunction with low-density parity-check codes is able to mitigate the effects of fading. The closed-form bit-error rate expressions of this scheme over independent and non-identically distributed and independent and identically distributed flat Rayleigh fading channels are derived using the extrinsic information transfer chart and Gaussian approximation. The derived expressions are compared with simulation results as well as the Eb/N0 threshold using density evolution (DE). They are in good agreement with simulation results and have the advantage of reduced computational complexity over DE.