Combined equalization and coding using precoding

Recently developed techniques that achieve the joint objectives of increasing the signaling rate so as to use the maximum possible channel bandwidth, and then using powerful equalization techniques to cope with the resulting distortion are reviewed. These techniques generalize the Tomlinson-Harashima precoding techniques, which were proposed more than 20 years ago. The principal classes of classical equalization techniques are described, and Tomlinson-Harashima precoding is introduced. It is shown that precoding combines nicely with coded modulation and with a technique known as shaping. It is also shown that, in principle, optimized combinations of coding, shaping, and precoding can achieve nearly the channel capacity of any strictly band-limited, high-SNR Gaussian channel, and in practice can approach capacity within about 3 dB or less.