Coded Caching based on Combinatorial Designs

We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called \textit{cache}) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. In this work, we propose a binary matrix model to construct the coded caching scheme. The ones in such a \textit{caching matrix} indicate uncached subfiles at the users. Identity submatrices of the caching matrix represent transmissions in the delivery phase. Using this model, we then propose several novel constructions for coded caching based on the various types of combinatorial designs. While most of the schemes constructed in this work (based on existing designs) have a high cache requirement (uncached fraction being $\Theta(\frac{1}{\sqrt{K}})$ or $\Theta(\frac{1}{K})$, $K$ being the number of users), they provide a rate that is either constant or decreasing ($O(\frac{1}{K})$) with increasing $K$, and moreover require competitively small levels of subpacketization (being $O(K^i), 1\leq i\leq 3$), which is an extremely important parameter in practical applications of coded caching. We mark this work as another attempt to exploit the well-developed theory of combinatorial designs for the problem of constructing caching schemes, utilizing the binary caching model we develop.Comment: 10 pages, Appeared in Proceedings of IEEE ISIT 201

Association and correlation of thyroid dysfunction with anemia types in pregnant women of northern Andhra Pradesh, India

Background: Thyroid dysfunction is a common disorder in pregnancy along with anemia. But no study has evaluated the association between them. To estimate the prevalence of thyroid dysfunction and its association with anemia types in pregnant women during 1st trimester.Methods: Three hundred and eighty pregnant women with <12 weeks of gestational age were selected for the study with no history of thyroid dysfunction and anemia. All the pregnant women were classified into A, euthyroid and B, thyroid dysfunction groups. The B group was again subdivided into hypothyroid, subclinical hypothyroid (SCH), hyperthyroid according to nature of dysfunction. 5 ml of blood sample was collected from all subjects to analyse thyroid hormones and erythrocyte indices.Results: Out of 380 subjects, euthyroid was found to be 77.9%, and rest 22.1% were with thyroid dysfunction. Out of 84 thyroid dysfunction, hypothyroid was found to be 7.9%, SCH 13.9% and hyperthyroid was 0.3%. Out of 296 euthyroid women, anemia was identified in 97 pregnant women (32.8%) whereas in thyroid dysfunction women it was 43 women out of 84 (51.2%) which is a statistically significant. Significantly higher frequency of microcytic hypochromic anemia and normocytic normochromic anemia types were also found in thyroid dysfunction groups compared to euthyroid group (p<0.05). However, no significance between the thyroid dysfunction groups, Statistically significant difference was observed in the Hb concentration, RBC count, MCV, MCH and PCV between euthyroid and different thyroid dysfunction conditions (p<0.05). A statistically significant positive correlation was found between fT4 and erythrocyte indices.Conclusions: As fT4 and TSH correlated with erythrocyte indices, it is advisable to screen for thyroid dysfunction and vice versa so as to prevent the complications associated with anemia and thyroid dysfunction