## Electrical and Computer Engineering Publications

#### Title

On Computation Rates for Arithmetic Sum

#### Campus Units

Electrical and Computer Engineering

Article

#### Publication Version

Submitted Manuscript

2016

arXiv

1601.07228

#### 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 \textit{clumpy distribution}. We also demonstrate an achievable scheme that uses variable length network codes and in-network compression.

This preprint is from arXiv:1601.07228 [cs.IT]. Posted with permission.

The authors

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