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Signal sets matched to groups

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1 Author(s)
H. -A. Loeliger ; Inst. for Signal & Inf. Process., ETH-Zentrum, Zurich, Switzerland

Recently, linear codes over ZM (the ring of integers mod M) have been presented that are matched to M -ary phase modulation. The general problem of matching signal sets to generalized linear algebraic codes is addressed based on these codes. A definition is given for the notion of matching. It is shown that any signal set in N-dimensional Euclidean space that is matched to an abstract group is essentially what D. Slepian (1968) called a group code for the Gaussian channel. If the group is commutative, this further implies that any such signal set is equivalent to coded phase modulation with linear codes over ZM. Some further results on such signal sets are presented, and the signal sets matched to noncommutative groups and the linear codes over such groups are discussed

Published in:

IEEE Transactions on Information Theory  (Volume:37 ,  Issue: 6 )