Under the paradigm of caching, partial data is delivered before the actual requests of users are known. In this paper, this problem is modeled as a canonical distributed source coding problem with side information, where the side information represen
ts the users requests. For the single-user case, a single-letter characterization of the optimal rate region is established, and for several important special cases, closed-form solutions are given, including the scenario of uniformly distributed user requests. In this case, it is shown that the optimal caching strategy is closely related to total correlation and Wyners common information. Using the insight gained from the single-user case, three two-user scenarios admitting single-letter characterization are considered, which draw connections to existing source coding problems in the literature: the Gray--Wyner system and distributed successive refinement. Finally, the model studied by Maddah-Ali and Niesen is rephrased to make a comparison with the considered information-theoretic model. Although the two caching models have a similar behavior for the single-user case, it is shown through a two-user example that the two caching models behave differently in general.
In wireless sensor networks, various applications involve learning one or multiple functions of the measurements observed by sensors, rather than the measurements themselves. This paper focuses on type-threshold functions, e.g., the maximum and indic
ator functions. Previous work studied this problem under the collocated collision network model and showed that under many probabilistic models for the measurements, the achievable computation rates converge to zero as the number of sensors increases. This paper considers two network models reflecting both the broadcast and superposition properties of wireless channels: the collocated linear finite field network and the collocated Gaussian network. A general multi-round coding scheme exploiting not only the broadcast property but particularly also the superposition property of the networks is developed. Through careful scheduling of concurrent transmissions to reduce redundancy, it is shown that given any independent measurement distribution, all type-threshold functions can be computed reliably with a non-vanishing rate in the collocated Gaussian network, even if the number of sensors tends to infinity.
The Magnetic cloud boundary layer (BL) is a dynamic region formed by the interaction of the magnetic cloud (MC) and the ambient solar wind. In the present study, we comparatively investigate the proton and electron mean flux variations in the BL, in
the interplanetary reconnection exhaust (RE) and across the MC-driven shock by using the Wind 3DP and MFI data from 1995 to 2006. In general, the proton flux has higher increments at lower energy bands compared with the ambient solar wind. Inside the BL, the core electron flux increases quasi-isotropically and the increments decrease monotonously with energy from ~30% (at 18 eV) to ~10% (at 70 eV); the suprathermal electron flux usually increases in either parallel or antiparallel direction; the correlation coefficient of electron flux variations in parallel and antiparallel directions changes sharply from ~0.8 below 70 eV to ~0 above 70 eV. Similar results are also found for RE. However, different phenomena are found across the shock where the electron flux variations first increase and then decrease with a peak increment (>200%) near 100 eV. The correlation coefficient of electron flux variations in parallel and antiparallel directions is always around 0.8. The similar behavior of flux variations in BL and RE suggests that reconnection may commonly occur in BL. Our work also implies that the strong energy dependence and direction selectivity of electron flux variations, which are previously thought to have no enough relevance to magnetic reconnection, could be considered as an important signature of solar wind reconnection in the statistical point of view.
