  In this paper, fast-decodable lattice code constructions are designed for the
nonorthogonal amplify-and-forward (NAF) multiple-input multiple-output (MIMO)
channel. The constructions are based on different types of algebraic
structures, e.g. quaternion division algebras. When satisfying certain
properties, these algebras provide us with codes whose structure naturally
reduces the decoding complexity. The complexity can be further reduced by
shortening the block length, i.e., by considering rectangular codes called less
than minimum delay (LMD) codes.
