various approaches have been proposed to improve the bounds on rate-memory tradeoff for the bottleneck network. Several caching schemes have been proposed in [@DBLP:journals/corr/Chen14h; @wan2016caching; @sahraei2016k; @tian2016caching; @amiri2016fundamental; @amiri2016coded; @yu2016exact; @gomez2016fundamental], and converse bounds have also been introduced in [@ghasemi15; @lim2016information; @sengupta15; @DBLP:journals/corr/WangLG16; @tian2016symmetry; @prem2015critical]. For the case, where the prefetching is uncoded, the exact rate-memory tradeoff for both peak and average rate (under uniform file popularity) and for both centralized and decentralized settings have been established in [@yu2016exact]. However, for the general case, where the cached content can be an arbitrary function of the files in the database, the exact characterization of the tradeoff remains open. In this case, the state of the art is an approximation within a factor of $4$ for peak rate [@ghasemi15] and $4.7$ for average rate under uniform file popularity [@lim2016information].

In this paper, we improve the approximation on characterizing the rate-memory tradeoff by proving new information-theoretic converse bounds, and achieving an approximation within a factor of $2.00884$, for both the *peak rate* and the *average rate* under uniform file popularity. These converse bounds hold for the general information theoretic framework, in the sense that there is no constraint on the caching or delivery 