Journal ArticleDOI
Signal sets matched to groups
TLDR
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 and that any such signal set is equivalent to coded phase modulation with linear codes over Z/sub M/.Abstract:
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. >read more
Citations
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Journal ArticleDOI
Geometrically uniform codes
TL;DR: Most known good classes of signal space codes are shown to be generalized coset codes, and therefore geometrically uniform, including lattice-type trellis codes based on lattice partitions Lambda / Lambda ' such that Z/sup N// Lambda/ Lambda '/4Z/Sup N/ is a lattice partition chain.
Journal ArticleDOI
The dynamics of group codes: state spaces, trellis diagrams, and canonical encoders
G.D. Forney,M.D. Trott +1 more
TL;DR: If C is complete and strongly controllable, then a minimal encoder in controller canonical (feedbackfree) form may be constructed from certain sets of shortest possible code sequences, called granules.
Book
A Foundation in Digital Communication
TL;DR: This systematic and insightful book – with over 300 exercises – is ideal for graduate courses in digital communication, and for anyone asking “why” and not just “how.”
Journal ArticleDOI
Convolutional codes over groups
TL;DR: The first part, which covers fundamental notions such as minimality and observability, is semi-tutorial in that most definitions are already standard (within the modern behavioral theory), as are some of the formally stated results.
Dissertation
Auditory group theory with applications to statistical basis methods for structured audio
TL;DR: Thesis (Ph. D.)--Massachusetts Institute of Technology, Program in Media Arts & Sciences, 1998.
References
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Journal ArticleDOI
Communication in the presence of noise
TL;DR: A method is developed for representing any communication system geometrically and a number of results in communication theory are deduced concerning expansion and compression of bandwidth and the threshold effect.
Journal ArticleDOI
Coset codes. II. Binary lattices and related codes
TL;DR: The family of Barnes-Wall lattices and their principal sublattices, which are useful in constructing coset codes, are generated by iteration of a simple construction called the squaring construction, and are represented by trellis diagrams that display their structure and interrelationships and that lead to efficient maximum-likelihood decoding algorithms.
Journal ArticleDOI
Geometrically uniform codes
TL;DR: Most known good classes of signal space codes are shown to be generalized coset codes, and therefore geometrically uniform, including lattice-type trellis codes based on lattice partitions Lambda / Lambda ' such that Z/sup N// Lambda/ Lambda '/4Z/Sup N/ is a lattice partition chain.
Permutation modulation
TL;DR: A class of codes and decoders is described for transmitting digital information by means of bandlimited signals in the presence of additive white Gaussiau noise, called permutation modulation, which has many desirable features.
Journal ArticleDOI
Group codes for the Gaussian channel
TL;DR: A decomposition theorem shows every group code to be equivalent to a direct sum of certain basic group codes generated by real-irreducible representations of a finite group associated with the code.