[论文解读] Combination Networks with Caches: Novel Inner and Outer Bounds with Uncoded Cache Placement.

Kai Wan, Mingyue Ji+2 more|arXiv (Cornell University)|Jan 24, 2017

Cooperative Communication and Network Coding被引用 3

一句话总结

该论文针对采用未编码缓存放置的组合网络，提出了新颖的内界与外界界，通过广义次模不等式推导出更紧致的对偶界。该研究提出了一类阶次最优的缓存方案，利用网络结构消除干扰，在数值评估中优于现有最先进方案。

ABSTRACT

Caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the user's local cache memory. For the shared-link network with end-user-caches, Maddah-Ali and Niesen proposed a two-phase coded caching strategy, referred to as MAN. In practice, users may communicate with the server through intermediate relays. This paper studies the tradeoff between the memory size M and the download time / rate R for networks where a server with N files is connected to H relays (without caches), which in turns are connected to K users equipped with caches of size M files. When each user is connected to a different subset of r relays, i.e., $K=\binom{H}{r}$, the system is referred to as a combination network with end-user-caches. In this work, converse bounds are derived for the practically motivated case of uncoded cache contents, that is, bits of the various files are directly copied in the user caches without any coding. In this case, once the cache contents and the user demands are known, the problem reduces to a general index coding problem. This paper shows that relying on a well known acyclic index coding converse bound results in bounds that are not tight for combination networks with end-user-caches and provides two novel ways to derive the tightest known converse bounds to date. As a result of independent interest, an inequality that generalizes the well-known sub-modularity of entropy is derived. Several novel caching schemes are proposed, based on the MAN cache placement. These schemes leverage the structure of the combination network and perform interference elimination at the end-users. The proposed schemes are proved: (i) to be (order) optimal for some parameters regimes of (N,M,H,r) with or without the constraint of uncoded cache placement, and (ii) to outperform the state-of-the-art schemes in numerical evaluations.

研究动机与目标

• 解决端用户缓存与未编码放置下组合网络的缓存-速率权衡问题。
• 为实际的未编码缓存内容情况，推导出比现有方法更紧致的对偶界。
• 设计利用网络拓扑结构以在终端用户处消除干扰的新颖缓存方案。
• 在各种参数配置下，建立阶次最优性并实现相对于最先进方案的性能提升。

提出的方法

• 通过将熵的次模性推广至适用于组合网络中的索引编码问题，推导出一种新颖的对偶界。
• 以已知的无环索引编码对偶界为基础，但通过改进使其在未编码缓存放置情况下获得更紧致的结果。
• 提出基于Maddah-Ali与Niesen（MAN）缓存放置策略的缓存方案，并针对组合网络结构进行适配。
• 通过利用用户连接至多个中继的特性，在用户端实现干扰对齐与消除。
• 在缓存内容与用户需求固定后，将系统建模为一般索引编码问题进行分析。
• 通过数值评估验证性能，将所提方案与现有最先进方案进行对比。

实验结果

研究问题

• RQ1 能否为采用未编码缓存放置的组合网络，推导出比现有方法更紧致的对偶界？
• RQ2 具有多中继连接结构的组合网络，其网络结构如何实现缓存性能的提升？
• RQ3 广义次模性在推导缓存网络中索引编码问题更紧致边界的机制中起到何种作用？
• RQ4 能否设计出在未编码放置下实现阶次最优的缓存方案？
• RQ5 在交付速率与缓存利用率方面，所提方案与现有方案在数值上相比如何？

主要发现

• 所提出的对偶界是目前针对采用未编码缓存放置的组合网络最紧致的已知结果。
• 推导出一种广义次模不等式，将基于熵的边界适用范围扩展至索引编码问题。
• 所提出的缓存方案在特定参数范围（N, M, H, r）内，无论是否采用未编码放置，均实现了阶次最优。
• 数值评估表明，所提方案在交付速率方面优于现有最先进方案。
• 通过利用多中继连接结构，方案能有效消除终端用户处的干扰。
• 结果表明，当与结构化传输结合时，未编码缓存放置可在组合网络中实现近似最优性能。