Modulation and coding for linear Gaussian channels

TLDR

Shannon's capacity result for the linear Gaussian channel has posed a long‑standing challenge to researchers. This paper surveys how that challenge has been addressed over the past half century, including recent advances that enable approaching capacity on any linear Gaussian channel. The survey covers orthogonal minimum‑bandwidth modulation, binary and nonbinary coding for low‑ and high‑SNR regimes, and capacity‑approaching methods such as turbo coding, multilevel coding, and combined coding/precoding for intersymbol‑interference channels.

Abstract

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 minimum-bandwidth 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.