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In this paper, a unified approach for weighted Viterbi decoding is proposed to improve error rate performance in multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) systems with linear precoding. The MIMO-OFDM systems with limited feedback precoding, optimal linear precoding (eigenmode), and spatial multiplexing are considered as a unified framework. In the proposed method, the branch metric is weighted by using the signal to interference noise ratio (SINR) of the effective channel in soft decision Viterbi decoding. The proposed scheme can mitigate noise enhancement for the coherent zero-forcing (ZF) or minimum mean square error (MMSE) decoder in these coded systems. Two low complexity linear decoders based on ZF and MMSE are compared. Extensive simulations show that the proposed unified approach with low complexity exhibit excellent performance.