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In the class of systems with linear precoder and decision feedback equalizers (DFE) for zero-padded (ZP) multiple-input multiple-output (MIMO) frequency selective channels, existing optimal transceiver designs present two drawbacks. First, the optimal systems require a large number of feedback bits from the receiver to encode the full precoding matrix. Second, the full precoding matrix leads to complex computations. These disadvantages become more severe as the bandwidth (BW) efficiency increases. In this paper, we propose using block diagonal geometric mean decomposition (BD-GMD) to design the transceiver. Two new BD-GMD transceivers are proposed: the ZF-BD-GMD system, where the receiver is a zero-forcing DFE (ZF-DFE), and the MMSE-BD-GMD system, where the receiver is a minimum- mean-square-error DFE (MMSE-DFE). The BD-GMD systems introduced here have the following four properties: a) They use the block diagonal unitary precoding technique to reduce the required number of encoding bits and simplify the computation. b) For any block size, the BD-GMD systems are optimal within the family of systems using block diagonal unitary precoders and DFEs. As block size gets larger, the BD-GMD systems produce uncoded bit error rate (BER) performance similar to the optimal systems using unitary precoders and DFEs. c) For the two ZF transceivers (ZF-Optimal and ZF-BD-GMD) and the two MMSE transceivers (MMSE-Optimal and MMSE-BD-GMD), the average BER degrades as the BW efficiency increases. d) In the case of single-input single-output (SISO) channels, the BD-GMD systems have the same performance as those of the lazy precoder transceivers. These properties make the proposed BD-GMD systems more favorable designs in practical implementation than the optimal systems.