In the class of systems with linear precoder and zero-forcing (ZF) DFE for zero-padded MIMO frequency selective channels, existing optimal transceiver designs present two major drawbacks. First, the optimal system requires a large number of bits to encode the full precoding matrix. Second, the full precoding matrix leads to complex computations. These disadvantages become more severe as bandwidth (BW) efficiency increases. In this article, we propose using the block diagonal geometric mean decomposition (BD-GMD) technique to design an alternative transceiver. The proposed ZF-BD-GMD system uses a block diagonal orthogonal precoder matrix structure to reduce the required number of encoding bits and simplifies the computation. While solving the current optimal system's drawbacks, the ZF-BD-GMD system also produces a similar bit error rate (BER) performance when the block size is large. In other words, the ZF-BD-GMD system is asymptotically optimal in the class of communication systems with linear precoder and ZF-DFE receiver. 1