New trellis codes based on lattices and cosets

Abstract

A new technique is proposed for constructing trellis codes. which provides an alternative to Ungerboeck's method of "set partitioning." The new codes use a signal constellation consisting of points from an <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -dimensional lattice <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Lambda</tex> , with an equal number of points from each coset of a sublattice <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Lambda '</tex> . One part of the input stream drives a generalized convolutional code whose outputs are cosets of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\Lambda '</tex> , while the other part selects points from these cosets. Several of the new codes are better than those previously known.