Characterizing the Rate-Memory Tradeoff in Cache Networks Within a Factor of 2

We consider a basic caching system, where a single server with a database of <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> files (e.g., movies) is connected to a set of <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> users through a shared bottleneck link. Each user has a local cache memory with a size of <inline-formula> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> files. The system operates in two phases: a placement phase, where each cache memory is populated up to its size from the database, and a following delivery phase, where each user requests a file from the database, and the server is responsible for delivering the requested contents. The objective is to design the two phases to minimize the load (peak or average) of the bottleneck link. We characterize the rate-memory tradeoff of the above caching system within a factor of 2.00884 for both the peak rate and the average rate (under uniform file popularity), improving the state of the arts that are within a factor of 4 and 4.7, respectively. Moreover, in a practically important case where the number of files (<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>) is large, we exactly characterize the tradeoff for systems with no more than five users and characterize the tradeoff within a factor of 2 otherwise. To establish these results, we develop two new converse bounds that improve over the state of the art.

[1]  Michael Gastpar,et al.  K users caching two files: An improved achievable rate , 2016, 2016 Annual Conference on Information Science and Systems (CISS).

[2]  Robert E. Tarjan,et al.  Amortized efficiency of list update and paging rules , 1985, CACM.

[3]  Zhi Chen.  Fundamental Limits of Caching: Improved Bounds For Small Buffer Users , 2014, ArXiv.

[4]  Michèle Wigger,et al.  Noisy Broadcast Networks With Receiver Caching , 2016, IEEE Transactions on Information Theory.

[5]  Mohammad Ali Maddah-Ali,et al.  Cache-aided interference management in wireless cellular networks , 2017, 2017 IEEE International Conference on Communications (ICC).

[6]  Jesús Gómez-Vilardebó.  Fundamental Limits of Caching: Improved Bounds with Coded Prefetching , 2016, ArXiv.

[7]  Urs Niesen,et al.  Coded Caching With Nonuniform Demands , 2017, IEEE Transactions on Information Theory.

[8]  Urs Niesen,et al.  Cache-aided interference channels , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[9]  T. Charles Clancy,et al.  Improved approximation of storage-rate tradeoff for caching via new outer bounds , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[10]  Mohammad Mohammadi Amiri,et al.  Fundamental Limits of Coded Caching: Improved Delivery Rate-Cache Capacity Trade-off , 2016 .

[11]  Urs Niesen,et al.  Decentralized coded caching attains order-optimal memory-rate tradeoff , 2013, 2013 51st Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[12]  Hooshang Ghasemi,et al.  Improved lower bounds for coded caching , 2015, 2015 IEEE International Symposium on Information Theory (ISIT).

[13]  Kai Wan.  On Caching with More Users than Files , 2018 .

[14]  Petros Elia,et al.  Fundamental limits of cache-aided wireless BC: Interplay of coded-caching and CSIT feedback , 2015, 2016 54th Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[15]  Michael Gastpar,et al.  A new converse bound for coded caching , 2016, 2016 Information Theory and Applications Workshop (ITA).

[16]  Michael Gastpar,et al.  Information theoretic caching: The multi-user case , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[17]  A. Salman Avestimehr,et al.  Cache-Aided Interference Management in Wireless Cellular Networks , 2019, IEEE Transactions on Communications.

[18]  Suhas N. Diggavi,et al.  Multi-level coded caching , 2014, 2014 IEEE International Symposium on Information Theory.

[19]  Xinbing Wang,et al.  Coded caching under arbitrary popularity distributions , 2015, 2015 Information Theory and Applications Workshop (ITA).

[20]  Giuseppe Caire,et al.  Fundamental Limits of Caching in Wireless D2D Networks , 2014, IEEE Transactions on Information Theory.

[21]  Suhas N. Diggavi,et al.  Hierarchical coded caching , 2014, 2014 IEEE International Symposium on Information Theory.

[22]  A. Salman Avestimehr,et al.  The Exact Rate-Memory Tradeoff for Caching With Uncoded Prefetching , 2016, IEEE Transactions on Information Theory.

[23]  Chao Tian,et al.  Symmetry, Outer Bounds, and Code Constructions: A Computer-Aided Investigation on the Fundamental Limits of Caching , 2016, 2017 IEEE International Symposium on Information Theory (ISIT).

[24]  Mohammad Ali Maddah-Ali,et al.  Fundamental limits of cache-aided interference management , 2016, 2016 IEEE International Symposium on Information Theory (ISIT).

[25]  Urs Niesen,et al.  Fundamental Limits of Caching , 2014, IEEE Trans. Inf. Theory.

[26]  Jaime Llorca,et al.  Order-Optimal Rate of Caching and Coded Multicasting With Random Demands , 2015, IEEE Transactions on Information Theory.

[27]  Urs Niesen,et al.  Online coded caching , 2014, ICC.

[28]  Deniz Gündüz,et al.  Coded caching for a large number of users , 2016, 2016 IEEE Information Theory Workshop (ITW).

[29]  Mohammad Ali Maddah-Ali,et al.  Characterizing the rate-memory tradeoff in cache networks within a factor of 2 , 2017, 2017 IEEE International Symposium on Information Theory (ISIT).