Characterizing Linear Memory-Rate Tradeoff of Coded Caching: The $(N,K)=(3,3)$ Case

We consider the cache problem introduced by Maddah-ali and Niesen [1] for the $(N,K)=(3,3)$ case, and use the computer-aided approach to derive the tight linear memory-rate trade-off. Two lower bounds $10M+6R\geq 15$ and $5M+4R\geq 9$ are proved, which are non-Shannon type. A coded linear scheme of point $(M,R)=(0.6,1.5)$ is constructed with the help of symmetry reduction and brute-force search.