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The Differential Encoding of Coset Codes by Algebraic Methods

  • A. R. Calderbank
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 20)

Abstract

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 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 90°. We describe the structure of coset codes and an algebraic method of resolving this phase ambiguity.

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Copyright information

© Springer-Verlag New York, Inc. 1990

Authors and Affiliations

  • A. R. Calderbank
    • 1
  1. 1.AT&T Bell LaboratoriesMurray HillUSA

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