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Block-by-block transceivers are commonly used to simplify the task of transmitting data over dispersive channels. In this paper, we consider the design of the transmitter-receiver pair in a block-by-block system which employs successive detection and interference cancellation at the receiver. (Such receivers are sometimes called block-decision feedback equalizers). We derive lower bounds on the mean-square error (MSE) of the equalizer's output and the bit-error rate (BER) at moderate-to-high SNR (in the absence of error propagation). These lower bounds guide us towards a closed form expression for a transceiver whose performance is close to these lower bounds. Simulation studies indicate that our transceiver performs significantly better than standard transceivers and retains its performance advantages in the presence of error propagation.