Summary: We study the joint optimization problem of a transmitter with multiple transmit antennas and a receiver with multiple receive antennas in a narrow-band communication system. We discuss the problem of designing a pre-filter at the transmitter, a post-filter at the receiver, and a bit allocation pattern to multiple symbols in the sense of minimizing the average bit error rate. With the optimized filters and the bit allocation, we could realize high efficiency and high data rate in band-limited channels.