  Lattices are deceptively simple mathematical structures that have become
indispensable for code design for physical layer communications. While
lattice-related problems are interesting in their own right, the usefulness of
these discrete structures in wireless communications provides additional
motivation for their study and enables a multidisciplinary line of research.
  This thesis is devoted to the study of lattice code design for physical layer
communications. Modern wireless communication networks are required to
accommodate significantly varied types of mobile devices, differing in
available computational power or number of equipped antennas. Additionally, the
density of the networks increases rapidly, and many communication protocols
diverge from the classical direct point-to-point transmission in favor of
allowing for intermediate relays to process and forward data. An important
consequence of this shift towards more sophisticated transmission protocols is
that traditional well-performing codes become futile for modern communications,
thus the study and development of novel codes is called for.
  Yet, however involved a transmission protocol may be, the characteristics of
the physical medium, i.e., the wireless channel, stay unaffected. It is thus
natural that an underlying lattice structure for code design remains crucial.
This thesis consists of several articles considering lattice code design for
four different communication settings relevant in modern wireless
communications.
