Coded Caching with Linear Coded Placement: Exact Tradeoff for the Three User Case

This paper studies the optimal memory-load trade-off in a coded caching system with K = 3 users under the constraint that the contents in the local caches are the result of encoding the files by a linear code. This setting generalizes past work that had established the optimal tradeoff under uncoded placement. Let N be the number of files.For K = N = 3 the optimal tradeoff under linear coded placement is shown to have a corner point in the low memory regime that was unknown before this work, which is actually optimal without any restrictions on the placement. For K = 3, N ≥ 4, the optimal tradeoff under linear coded placement is shown to be attained by uncoded placement. As a consequence of this result together with past optimality results, it is an open question whether non-linear coded placement would outperform the tradeoff derived in this work for the memory regime M ∈ (1/2, 1) for N = 3, and M ∈ (0, N/3) for K = 3, N ∈ {4, 5}.