Publication

Function computation over linear channels

Christina Fragouli, Lorenzo Keller, Nikhil Karamchandani
2010
Conference Papers

Abstract

We consider multiple non-colocated sources commu- nicating over a network to a common sink. We assume that the network operation is fixed, and its end result is to convey a fixed linear deterministic transformation of the source data to the sink. This linear transformation is known both at the sources and at the sink. We are interested in the problem of function computation over such networks. We design communication protocols that can perform computation without modifying the network operation, by appropriately selecting the codebook that the sources employ to map their measurements to the data they send over the network.

Official source

https://infoscience.epfl.ch/entities/publication/3bdbab89-4707-4714-8aa7-8bb5ec3528ab

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Christina Fragouli, Lorenzo Keller, Nikhil Karamchandani
2010
Conference Papers

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/3bdbab89-4707-4714-8aa7-8bb5ec3528ab

About this result

Related concepts (18)

Theory of computation

In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation, using an algorithm, how efficiently they can be solved or to what degree (e.g., approximate solutions versus precise ones). The field is divided into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question: "What are the fundamental capabilities and limitations of computers?".

Linear map

In mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .

Affine transformation

In Euclidean geometry, an affine transformation or affinity (from the Latin, affinis, "connected with") is a geometric transformation that preserves lines and parallelism, but not necessarily Euclidean distances and angles. More generally, an affine transformation is an automorphism of an affine space (Euclidean spaces are specific affine spaces), that is, a function which maps an affine space onto itself while preserving both the dimension of any affine subspaces (meaning that it sends points to points, lines to lines, planes to planes, and so on) and the ratios of the lengths of parallel line segments.

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