New Geometrically Uniform codes using QAM which improve the performance/complexity tradeoff of 2D codes

Given a signal set whose Geometrically Uniform (GU) partition allows binary isometric labelings, a GU code ( C g,C) is determined by a binary label code C and a binary isometric labeling g. Two such codes are defined to be equivalent if they have the same transmission rate and the same transfer function T (D) . It is then shown that all binary isometric labelings for the given GU partition are equally good so that it is enough to search for good codes using a single fixed isometric labeling. It is also shown that the set of codes with the same number of states is partitioned into subsets of equivalent codes. This allows a fast search algorithm which rejects all but one of codes that are equivalent to each other. New 128-, 256-, and 512-state codes using QAM constellations are given to improve the performance/complexity tradeoff of 2D trellis codes. © 2008 IEEE.