Campus Units
Electrical and Computer Engineering
Document Type
Conference Proceeding
Conference
2016 IEEE International Symposium on Information Theory (ISIT)
Publication Version
Accepted Manuscript
Link to Published Version
http://dx.doi.org/10.1109/ISIT.2016.7541720
Publication Date
2016
Journal or Book Title
2016 IEEE International Symposium on Information Theory (ISIT)
First Page
2354
Last Page
2358
DOI
10.1109/ISIT.2016.7541720
Conference Title
2016 IEEE International Symposium on Information Theory (ISIT)
Conference Date
July 10–15, 2016
City
Barcelona, Spain
Abstract
For zero-error function computation over directed acyclic networks, existing upper and lower bounds on the computation capacity are known to be loose. In this work we consider the problem of computing the arithmetic sum over a specific directed acyclic network that is not a tree. We assume the sources to be i.i.d. Bernoulli with parameter 1/2. Even in this simple setting, we demonstrate that upper bounding the computation rate is quite nontrivial. In particular, it requires us to consider variable length network codes and relate the upper bound to equivalently lower bounding the entropy of descriptions observed by the terminal conditioned on the function value. This lower bound is obtained by further lower bounding the entropy of a so-called clumpy distribution. We also demonstrate an achievable scheme that uses variable length network codes and in-network compression.
Rights
Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
Copyright Owner
IEEE
Copyright Date
2016
Language
en
File Format
application/pdf
Recommended Citation
Tripathy, Ardhendu and Ramamoorthy, Aditya, "On computation rates for arithmetic sum" (2016). Electrical and Computer Engineering Conference Papers, Posters and Presentations. 11.
https://lib.dr.iastate.edu/ece_conf/11
Comments
This proceeding is from 2016 IEEE International Symposium on Information Theory, Barcelona, 2016, pp. 2354-2358. doi:10.1109/ISIT.2016.7541720. Posted with permission.