  The design of block codes for short information blocks (e.g., a thousand or
less information bits) is an open research problem that is gaining relevance
thanks to emerging applications in wireless communication networks. In this
paper, we review some of the most promising code constructions targeting the
short block regime, and we compare them with both finite-length performance
bounds and classical error-correction coding schemes. The work addresses the
use of both binary and high-order modulations over the additive white Gaussian
noise channel. We will illustrate how to effectively approach the theoretical
bounds with various performance versus decoding complexity tradeoffs.
