On Computation Rates for Arithmetic Sum
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.
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
2016 IEEE International Symposium on Information Theory, ISIT (2016: Jul. 10-15, Barcelona, Spain)
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10 Aug 2016