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Shannon's determination of the capacity of the linear Gaussian channel has posed a magnificent challenge to succeeding generations of researchers. This paper surveys how this challenge has been met during the past half century. Orthogonal minimumbandwidth modulation techniques and channel capacity are discussed. Binary coding techniques for low-signal-to-noise ratio (SNR) channels and nonbinary coding techniques for high-SNR channels are reviewed. Recent developments, which now allow capacity to be approached on any linear Gaussian channel, are surveyed. These new capacity-approaching techniques include turbo coding and decoding, multilevel coding, and combined coding/precoding for intersymbol-interference channels.

A new look is taken at maximum-likelihood sequence estimation in the presence of intersymbol interference. A uniform receiver structure for linear carrier-modulated data-transmission systems is derived which for decision making uses a modified version of the Viterbi algorithm. The algorithm operates directly on .the output signal of a complex matched filter and, in contrast to the original algorithm, requires no squaring operations; only multiplications by discrete pulse-amplitude values.are needed. Decoding of redundantly coded sequences is included in the consideration. The reason and limits for the superior error performance of the receiver over a conventional receiver employing zero-forcing equalization and symbol-by-symbol decision making are explained. An adjustment algorithm for jointly approximating the matched filter by a transversal filter, estimating intersymbol interference present at the transversal filter output, and controlling the demodulating carrier phase and the sample timing, is presented.

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