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This paper presents a method for jointly designing the transmitter-receiver pair in a block-by-block transmission system that employs minimum mean square error intra-block decision feedback detection. We provide a recursive closed-form expression for a transceiver which maximizes the Gaussian mutual information and also minimizes the bit error rate at moderate-to-high signal-to-noise ratios (in the absence of error propagation). The proposed design generates uncorrelated inputs to the decision device with equal signal-to-interference-and-noise ratios. These properties suggest that one can approach the capacity of the block transmission system using (independent instances of) the same (Gaussian) code for each element of the block. Our simulation studies indicate that the proposed transceiver performs significantly better than standard transceivers, and that it retains its performance advantages in the presence of error propagation.