Network functional compression

摘要: In this thesis, we consider different aspects of the functional compression problem. functional compression, the computation a function (or, some functions) sources is desired at the receiver(s). The rate region problem has been considered in literature under certain restrictive assumptions. Chapter 2 Thesis, problem for an arbitrary tree network and asymptotically lossless computations. particular, for one-stage networks, we compute rate-region network, derive a lower bound based on graph entropy. We introduce new condition colorings source random variables' characteristic graphs called coloring connectivity condition (C.C.C.). show that unlike mentioned Doshi et al., condition is necessary sufficient any achievable coding scheme based on colorings. also show that, entropy, entropy does not satisfy chain rule. For one stage trees with correlated sources, general independent sources, propose a modularized to perform arbitrarily closely derived bound. that in case achieve the bound, intermediate nodes should perform some computations. However, family functions random variables rule proper sets, it is have intermediate act like relays arbitrarily closely to 3 a multi-functional version side information, where receiver wants compute several with different information variables zero distortion. Our results are applicable receivers computing desired functions. define new concept named multi-functional which extension graph entropy defined by K6rner. that minimum rate for equal conditional variable given information. We achieve this rate. these proposed schemes, needs compute the (a which minimizes entropy) characteristic graph. general, finding NP-hard 4, we depending graph's structure, there interesting cases where finding entropy coloring not NP-hard, but tractable practical. of these cases, having non-zero joint probability condition distributions, desired function, can be solved in polynomial time. another case, if desired function quantization function, also tractable. general…