Optimal Linear Error Correcting Delivery Schemes for Two Optimal Coded Caching Schemes

For coded caching problems with small buffer sizes and the number of users no less than the amount of files in the server, an optimal delivery scheme was proposed by Chen, Fan, and Letaief in 2016. This scheme is referred to as the CFL scheme. In this paper, an extension to the coded caching problem where the link between the server and the users is error prone, is considered. The closed form expressions for average rate and peak rate of error correcting delivery scheme are found for the CFL prefetching scheme using techniques from index coding. Using results from error correcting index coding, an optimal linear error correcting delivery scheme for caching problems employing the CFL prefetching is proposed. Another scheme that has lower sub-packetization requirement as compared to CFL scheme for the same cache memory size was considered by J. Gomez-Vilardebo in 2018. An optimal linear error correcting delivery scheme is also proposed for this scheme.