On computation rates for arithmetic sum2016 IEEE International Symposium on Information Theory (ISIT)
Document TypeConference Proceeding
Conference2016 IEEE International Symposium on Information Theory (ISIT)
Publication VersionAccepted Manuscript
Link to Published Versionhttp://dx.doi.org/10.1109/ISIT.2016.7541720
Conference Title2016 IEEE International Symposium on Information Theory (ISIT)
Conference DateJuly 10–15, 2016
AbstractFor 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.
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Citation InformationArdhendu Tripathy and Aditya Ramamoorthy. "On computation rates for arithmetic sum" Barcelona, Spain2016 IEEE International Symposium on Information Theory (ISIT) (2016) p. 2354 - 2358
Available at: http://works.bepress.com/ardhendu-tripathy/1/