Successive Minimization of the State Complexity of theSelf - dual Lattices Using

This work presents a systematic method to successively minimize the state complexity of the self-dual lattices (in the sense that each section of the trellis has the minimum possible number of states xing its preceding coordinates). This is based on representing the lattice on an orthogonal coordinate system corresponding to the Gram-Schmidt (GS) vectors of a Korkin-Zolotarev (KZ) reduced basis. As part of the computations, we give expressions for the GS vectors of a KZ basis of the K12, 24, and BWn lattices. It is also shown that for the complex representation of the 24 and the BWn lattices over the set of the Gaussian integers, we have: (i) the corresponding GS vectors are along the standard coordinate system, and (ii) the branch complexity at each section of the resulting trellis meets a certain lower bound. This results in a very eecient trellis representation for these lattices over the standard coordinate system.