[论文解读] Combination Networks with End-user-caches: Novel Achievable and Converse Bounds under Uncoded Cache Placement

Kai Wan, Daniela Tuninetti+2 more|arXiv (Cornell University)|Jan 24, 2017

Caching and Content Delivery参考文献 23被引用 11

一句话总结

本文针对采用非编码缓存放置的端用户缓存组合网络，提出了新颖的可实现与反向边界，利用网络拓扑结构推导出比以往方法更紧的边界。它提出了一种新型反向边界，优于现有方法，并设计了利用干扰消除与网络结构的阶次最优缓存方案，在某些参数范围内实现了与最优负载相差不超过4/3的乘法间隙。

ABSTRACT

Caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the users' local caches. For the shared-link network with end-user-caches, Maddah-Ali and Niesen proposed a two-phase coded caching strategy. In practice, users may communicate with the server through intermediate relays. This paper studies the tradeoff between the memory size $M$ and the network load $R$ for networks where a server with $N$ files is connected to $H$ relays (without caches), which in turn are connected to $K$ users equipped with caches of $M$ 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 {\\it combination network with end-user-caches}. In this work, converse bounds are derived for the practically motivated case of {\\it uncoded} cache contents, that is, bits of the various files are directly pushed into 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 converse bounds that are not tight for combination networks with end-user-caches. A novel converse bound that leverages the network topology is proposed, which is the tightest converse bound known 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 Maddah-Ali and Niesen cache placement. The proposed schemes are proved: (i) to be (order) optimal for some $(N,M,H,r)$ parameters regimes under 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

• 解决在非编码放置下，组合网络中缓存内存大小M与网络负载R之间的基本权衡问题。
• 克服现有反向边界（尤其是无环索引编码边界）在该网络模型中不够紧致的局限性。
• 设计利用组合网络拓扑结构并可在端用户实现干扰消除的新型缓存方案。
• 通过引入网络特定的结构约束，建立更紧致的反向边界，优于先前的最先进成果。

提出的方法

• 提出一种显式利用组合网络拓扑结构的新型反向边界，优于无环索引编码反向边界。
• 推导出支持新反向边界推导的熵的一般化次模不等式。
• 基于Maddah-Ali与Niesen（MAN）缓存放置策略设计缓存方案，并根据组合网络的中继结构进行适配。
• 通过在多个中继间对传输信号进行对齐，实现在端用户处的干扰消除技术。
• 采用线性规划形式化方法推导最小负载的边界，整合用户需求与缓存内容的约束条件。
• 通过数值评估验证性能，结果表明在非编码放置下优于现有最先进方案。

实验结果

研究问题

• RQ1 能否通过利用网络拓扑结构，为采用非编码放置的端用户缓存组合网络推导出更紧致的反向边界？
• RQ2 为何现有的无环索引编码反向边界在组合网络中端用户缓存场景下无法保持紧致性？
• RQ3 在组合网络中采用非编码缓存放置时，何种缓存方案可实现阶次最优性能？
• RQ4 所提出的反向边界与切集边界及其他已知边界相比，在紧致性方面表现如何？
• RQ5 在不同参数范围内，所提出的可实现方案与最优负载之间的乘法间隙是多少？

主要发现

• 所提出的反向边界是目前针对采用非编码放置的端用户缓存组合网络最紧致的已知边界，显著优于无环索引编码反向边界。
• 推导出一个关于熵的一般化次模不等式，该不等式具有独立的理论价值，并支持新反向边界的推导。
• 所提出的缓存方案在某些参数范围内实现阶次最优性能，与最优负载的乘法间隙被限制在4/3以内。
• 数值评估表明，所提方案在负载降低方面优于现有最先进方案。
• 当缓存大小满足 M ≤ N/K 时，所提方案在最优负载的4/3倍因子内实现阶次最优，且随着 r 增大，间隙减小。
• 结果表明切集边界与所提反向边界的比值在 1 + t/r 以内，证实了在高缓存容量区域中该方案的近似最优性。