Broadcast Caching Networks with Two Receivers and Multiple Correlated Sources

The correlation among the content distributed across a cache-aided broadcast network can be exploited to reduce the delivery rate over the broadcast link. This paper considers a two-user three-file network with correlated content, and studies its fundamental limits for the worst-case demand. A class of schemes based on a two-step source coding approach is proposed to exploit the content correlation and the content distribution among local caches, consecutively. Files are first compressed using a Gray-Wyner-type source coding, and then cached and delivered using a combination of correlation-unaware cache-aided coded multicast schemes. An optimal caching scheme is proposed for a two-user network where users request two out of three independent files, and is later used as a basis for designing the second step of the Gray-Wyner-based scheme. A lower bound on the optimal peak rate-memory trade-off is derived, which is used to evaluate the performance of the proposed scheme. It is shown that the two-step scheme achieves the lower bound for large cache capacities and is within half of the joint entropy of two of the files given the third file for all other cache sizes.