Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework considers non-Shannon-type inequalities which are valid for representable polymatroids (and hence for linear codes), and leverages symmetric structure and problem-specific constraints of coded caching to reduce the complexity of the linear program. The derived converse bounds are tighter compared to previous known analytic methods, and prove the optimality of some achievable memory-load tradeoff points under the constraint of linear coding placement and delivery. These results seem to indicate that small, structured demand subsets combined with minimal common information constructions may be sufficient to characterize optimal tradeoffs under linear coding.

翻译：受田与曹和徐先前工作的启发，本文提出了一种高效的计算机辅助框架，用于表征线性编码约束下编码缓存系统的基本极限。该框架考虑了适用于可表示多拟阵（因而适用于线性编码）的非香农型不等式，并利用编码缓存的对称结构和问题特定约束来降低线性规划的复杂度。推导出的逆界比先前已知的解析方法更紧，并证明了在线性编码放置与传输约束下部分可达内存-负载权衡点的最优性。这些结果表明，结合最小公共信息构建的小型结构化需求子集可能足以表征线性编码下的最优权衡。