On Computation Rates for Arithmetic Sum

Author

Ardhendu S. Tripathy, Missouri University of Science and TechnologyFollow
Aditya Ramamoorthy

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.

Recommended Citation

A. S. Tripathy and A. Ramamoorthy, "On Computation Rates for Arithmetic Sum," IEEE International Symposium on Information Theory - Proceedings, pp. 2354 - 2358, Institute of Electrical and Electronics Engineers (IEEE), Aug 2016.

The definitive version is available at https://doi.org/10.1109/ISIT.2016.7541720

Meeting Name

2016 IEEE International Symposium on Information Theory, ISIT (2016: Jul. 10-15, Barcelona, Spain)

Department(s)

Computer Science

Comments

This work was supported in part by the National Science Foundation by grants CCF- 1320416, CCF- 1149860 and DMS-1120597.

International Standard Book Number (ISBN)

978-150901806-2

International Standard Serial Number (ISSN)

2157-8095

Document Type

Article - Conference proceedings

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2016 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

10 Aug 2016