Signal sets matched to groups

Recently, linear codes over Z/sub M/ (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...

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Bibliographic Details
Published in:IEEE transactions on information theory 1991-11, Vol.37 (6), p.1675-1682
Main Author: Loeliger, H.-A.
Format: Article
Language:English
Subjects:
Applied sciences
Exact sciences and technology
Galois fields
Gaussian channels
Hamming distance
Hamming weight
Information, signal and communications theory
Linear code
Linearity
Modulation coding
Phase modulation
Signal processing
Signal to noise ratio
Telecommunications and information theory
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Summary:Recently, linear codes over Z/sub M/ (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 Z/sub M/. 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.< >
ISSN:0018-9448
1557-9654
DOI:10.1109/18.104333