Large gains in the rate of cache-aided broadcast communication are obtained using coded caching, but to obtain this most existing centralized coded caching schemes require that the files at the server be divisible into a large number of parts (this number is called subpacketization). In fact, most schemes require the subpacketization to be growing asymptotically as exponential in $\sqrt[\leftroot{-1}\uproot{1}r]{K}$ for some positive integer $r$ and $K$ being the number of users. On the other extreme, few schemes having subpacketization linear in $K$ are known; however, they require large number of users to exist, or they offer only little gain in the rate. In this work, we propose two new centralized coded caching schemes with low subpacketization and moderate rate gains utilizing projective geometries over finite fields. Both the schemes achieve the same asymptotic subpacketization, which is exponential in $O((\log K)^2)$ (thus improving on the $\sqrt[\leftroot{-1}\uproot{1}r]{K}$ exponent). The first scheme has a larger cache requirement but has at most a constant rate (with increasing $K$), while the second has small cache requirement but has a larger rate. As a special case of our second scheme, we get a new linear subpacketization scheme, which has a more flexible range of parameters than the existing linear subpacketization schemes. Extending our techniques, we also obtain low subpacketization schemes for other multi-receiver settings such as distributed computing and the cache-aided interference channel. We validate the performance of all our schemes via extensive numerical comparisons. For a special class of symmetric caching schemes with a given subpacketization level, we propose two new information theoretic lower bounds on the optimal rate of coded caching.
翻译:缓存辅助广播通信率的大幅增益是使用编码缓存获得的,但为了获得这种现有的大多数中央编码缓存计划,服务器的文档需要可分化成大量部件(这个数字被称为子包装 ) 。 事实上, 多数计划要求子包装化的速率增长与 $\ sqrt[\\ leftroot{-1 ⁇ uproot{1}{K}}}}K} 的指数增长一样。 对于某些正整整数低的美元和 $K美元( 用户数) 的用户数。 在另一个极端方面, 很少有以美元为基元的子包装线性线性计划; 然而, 服务器的文档需要大量用户存在, 或只能提供少量的增益 。 在这项工作中, 我们提出了两个新的中央编码化的缓存计划, 两种方案都取得了相同的, 以美元( ( log K) ) 和 美元( ) 新的递缩递增的递增的递增的货币计划 。