We construct irreducible representations of affine Khovanov-Lauda-Rouquier
algebras of arbitrary finite type. The irreducible representations arise as
simple heads of appropriate induced modules, and thus our construction is
similar to that of Bernstein and Zelevinsky for affine Hecke algebras of type
A. The highest weights of irreducible modules are given by the so-called good
words, and the highest weights of the 'cuspidal modules' are given by the good
Lyndon words. In a sense, this has been predicted by Leclerc.