Rate-Memory Trade-Off for Caching and Delivery of Correlated Sources

Abstract

This paper studies the fundamental limits of content delivery in a cache-aided broadcast network for correlated content generated by a discrete memoryless source with arbitrary joint distribution. Each receiver is equipped with a cache of equal capacity, and the requested files are delivered over a shared error-free broadcast link. A class of achievable correlation-aware schemes based on a two-step source coding approach is proposed. Library files are first compressed, and then cached and delivered using a combination of correlation-unaware multiple-request cache-aided coded multicast schemes. The first step uses Gray-Wyner source coding to represent the library via private descriptions and descriptions that are common to more than one file. The second step then becomes a multiple-request caching problem, where the demand structure is dictated by the configuration of the compressed library, and it is interesting in its own right. The performance of the proposed two-step scheme is evaluated by comparing its achievable rate with a lower bound on the optimal peak and average rate-memory tradeoffs in a two-file multiple-receiver network, and in a three-file two-receiver network. Specifically, in a network with two files and two receivers, the achievable rate matches the lower bound for a significant memory regime and it is within half of the conditional entropy of files for all other memory values.In the three-file two-receiver network, the two-step strategy achieves the lower bound for large cache capacities, and it is within half of the joint entropy of two of the sources conditioned on the third one for all other cache sizes.for the compression of requested files during the delivery phase. Alternatively, our work in [9] addresses the content dependency by first compressing the correlated library. A subset of the files, most representative of the library, are selected as references, referred to as I-files, and the remaining files are inter-compressed with respect to the selected files and referred to as P-files.This results in a compressed library where each file is made up of an I-file and a P-file, leading to a multiple-request caching problem. Differently from previous multiple-request schemes [4],[15]- [18], the demand in [9] has a specific structure dictated by the configuration of the resulting compressed library in terms of I-files and P-files. 3 The first information-theoretic characterization of the rate-memory trade-off in a cache-aided broadcast network with correlated content was studied in [10] for the setting of two files and two receivers, each equipped with a cache. This paper introduces an achievable two-step scheme that exploits content correlations by first jointly compressing the library files using the Gray-Wyner network [14], and then treating the compressed content as independent files. It is shown in [10] that this strategy is optimal for a large memory regime, while the gap to optimality is quantified for other memory values.Building on the idea introduced in [9] and [10], concurrent work i...

On Coded Caching with Correlated Files

“…However, in practice overlaps among different files is possible (e.g., videos, image streams, etc.). Coded caching with correlated files was considered in [4], where each subset of files has an exclusively common part; a caching scheme for two-file K−user system, and for three-file twouser system, was proved to be near-optimal for worst-case demands. In [5] the caching problem with correlated files, where the length of the common part among each files (referred to as a ' -block') is the same, was considered; each file contains N−1 −1 −blocks.…”

Decentralized Caching under Nonuniform File Popularity and Size: Memory-Rate Tradeoff Characterization

“…Besides the above works, decentralized coded caching has also been extended to other heterogeneous scenarios or system setups, including heterogeneous user profiles [34]- [37], correlated files [38], nonuniform cache sizes [19], heterogeneous distortion [39], [40], multi-antenna transmission and shared caches [41].…”

Coded Caching for Broadcast Networks with User Cooperation

“…Coded caching that jointly considers various heterogeneous aspects was studied in [ 17 ]. Other works on coded caching include, e.g., cache-aided noiseless multi-server network [ 18 ], cache-aided wireless/noisy broadcast networks [ 19 , 20 , 21 , 22 ], cache-aided relay networks [ 23 , 24 , 25 ], cache-aided interference management [ 26 , 27 ], coded caching with random demands [ 28 ], caching in combination networks [ 29 ], coded caching under secrecy constraints [ 30 ], coded caching with reduced subpacketization [ 31 , 32 ], the coded caching problem where each user requests multiple files [ 33 ], and a cache-aided broadcast network for correlated content [ 34 ], etc.…”