Hotplug Coded Caching: Uncoded versus Row-Wise Coded Placements

In the hotplug coded caching model, $K$ users fill their caches of size $M$ as a function of $N$ files, but only an unknown subset of $A\leq K$ users is active in the delivery phase. In all regimes where the optimal hotplug tradeoff is known, it depends only on $A$, not on $K$; whether this holds in general is open. We show that: (i) Under uncoded placement, YMA delivery with MAN placement, where offline users are assigned the demands of active users, is optimal. Hence, offline users cause a strict load penalty at intermediate memory sizes, while the MAN placement is optimal for every number of active users; (ii) Under row-wise placement (RWP), where each cache is a function of the user's own row of each file, every classical scheme can be embedded in a Reed-Solomon code. The resulting hotplug scheme has the tradeoff of the classical model with $A$ users, for every $A\leq K$: there is no load penalty, but the placement depends on $K$. We then derive a converse for RWP, which shows that: (a) for $2\leq N\leq A$, the scheme of Gomez-Vilardebo (GV) is RWP optimal for $AM\leq N/(N-1)$, which settles the RWP tradeoff for $N=2$; (b) YMA is RWP optimal at $AM=N$; and (c) for $N=A=3$, GV is RWP optimal for $M\leq 1$. Hence, the Reed-Solomon embeddings of these schemes are optimal among embedded RWP schemes.