The differential encoding of coset codes by algebraic methods.

A trellis code is a method of encoding a binary data stream as a sequence of real vectors that are transmitted over a noisy channel. Trellis codes are used in modems designed to achieve data rates of up to 19.2 kb/s on dial-up voice telephone lines. Coset codes are trellis codes based on lattices and cosets. The signal constellation is finite, and signal points are taken from a 2N-dimensional lattice L, with an equal number of points taken from each coset of a sublattice M. One part of the input data stream selects cosets of M in L and the other part selects points from those cosets. An important practical problem is that of channel phase shifts which cause a rotation of every 2-dimensional constituent of a 2N-dimensional signal through the same multiple of 90degrees. We describe the structure of coset codes and an algebraic method of resolving this phase ambiguity.