--- title: Hotplug Coded Caching url: https://www.emergentmind.com/topics/hotplug-coded-caching type: topic --- # Hotplug Coded Caching Searching arXiv for recent and foundational papers on hotplug coded caching and related dynamic/shared-cache variants. Hotplug coded caching denotes a family of coded-caching models in which cache placement is completed before the delivery-time participation pattern is known. In the literature, the term most often refers to a dedicated-cache system with \(K\) placed users but only \(K'\le K\) active users in delivery, so placement knows the value of \(K'\) but not the active set \(\mathcal I\in\binom{[K]}{K'}\). Closely related work uses an analogous late-binding model in shared-cache networks, where user-to-helper attachment is unknown during placement and revealed only afterward. In both interpretations, the central problem is to preserve coded-multicasting gain under uncertainty in who is online, which helper serves whom, or which caches remain accessible, without redoing placement after the actual delivery topology is revealed [2311.02856] [2404.06433] [2209.00299]. ## 1. Canonical model and scope In the dedicated-cache hotplug model, the server stores \(N\) files, serves \(K\) users over a shared link, and performs placement knowing that exactly \(K'\) users will later be active, but not which users those will be. Delivery begins after a subset \(\mathcal I\in\binom{[K]}{K'}\) appears and reveals demands. This differs from the original Maddah-Ali–Niesen setting, which assumes that all \(K\) users are active and that the server waits for all demands before transmission. Later privacy-oriented work keeps the same hotplug structure and denotes the active set by \(\mathcal A\in\Omega_{[K]}^{K'}\), with the remaining users offline [2404.06433] [2305.06518]. The literature also uses a broader hotplug interpretation for topological uncertainty. In the shared-cache model with helper nodes, one server serves \(K\) users through \(\Lambda\le K\) helper caches, each user attaches to exactly one helper, and the unknown quantity is the user-to-helper association rather than the active user subset. The case in which the association is unknown during placement and revealed only afterward is explicitly identified as the closest formalization of hotplug or dynamic attachment after placement in that setting [2209.00299]. This scope matters because not every dynamic coded-caching problem is hotplug coded caching in the same sense. Asynchronous-request models keep the user population fixed and let requests arrive at different times; dynamic centralized designs preserve incumbent users’ caches while onboarding new users across rounds; and adaptive-delivery schemes may assume arbitrary cache states at delivery time without modeling user arrival or departure during an episode. These are adjacent problems, but they solve different parts of the broader dynamical-caching design space [1907.06801] [1906.08539] [1912.04321]. ## 2. Array-based formulations The dominant combinatorial abstraction for dedicated-cache hotplug systems is the **hotplug placement delivery array (HpPDA)**. An HpPDA is a pair \((P,B)\) where \(P\) is an \(F\times K\) array of stars and nulls, with \(Z\) stars per column, and \(B\) is a \([K',F',Z',S]\)-PDA. The defining property is that for every active set \(\tau\subseteq[K]\), \(|\tau|=K'\), there exists a row subset \(\zeta\subseteq[F]\), \(|\zeta|=F'\), such that the restricted subarray \([P]_{\zeta\times\tau}\) has the same star pattern as \(B\). This gives a \((K,K',N)\) hotplug coded-caching scheme with subpacketization \(F'\), memory ratio \(M/N=Z/F'\), and rate \(R=S/F'\) by first splitting each file into \(F'\) parts, then applying an \([F,F']\) MDS code, placing coded subfiles according to \(P\), and running PDA delivery according to \(B\) on the realized active set [2311.02856]. A later refinement keeps the same HpPDA pair but changes the MDS dimension. For any \((K,K',F,F',Z,Z',S)\)-HpPDA, the scheme in [2404.06433] encodes each file from \(F'-Z'+Z\) source subfiles into \(F\) coded subfiles and achieves \[ \left(\frac{M}{N},R\right)=\left(\frac{Z}{F'-Z'+Z},\frac{S}{F'-Z'+Z}\right). \] The reason is structural: each active user already holds \(Z\) coded symbols from placement and receives \(F'-Z'\) additional coded symbols from delivery, so it accumulates \(F'-Z'+Z\) coded symbols, sufficient for MDS decoding. For the same HpPDA, this shifts the operating point to a lower cache-memory ratio than the earlier \(Z/F'\) normalization [2404.06433]. The same array methodology has been generalized in two directions. In two-layer hierarchical networks with mirror caches and user caches, the **hierarchical hotplug placement delivery array (HHPDA)** uses one array for mirror placement and local user structure, and one PDA for the active-user projection. The resulting scheme has mirror memory ratio \(M_1/N=Z_1/F'\), user memory ratio \(M_2/N=Z_2/F'\), first-layer load \(R_1=|\mathcal S|/F'\), and a second-layer load \(R_2\) determined by the local symbol sets induced at each mirror [2507.00727]. In combinatorial multi-access hotplug networks, a generalized HpPDA uses a cache-placement array \(P_c\), a derived user-access array \(P\), and a family of PDAs \(\{B_j\}_{j=1}^r\) indexed by the number of online caches accessible to a user. Under the decodability condition \(F'_j-Z'_j+Z_j\ge F'_r-Z'_r+Z\), it yields \[ \left(\frac{M}{N},R\right)=\left(\frac{Z_c}{Z+F'_r-Z'_r},\sum_{j=1}^r\frac{S_j}{Z+F'_r-Z'_r}\right) \] for the \((C,C',r,N)\) combinatorial multi-access hotplug model [2601.10503]. ## 3. Dedicated-cache scheme families A first major family is the **MAN-HpPDA** family, which shows that the Ma–Tuninetti hotplug construction can be represented as an HpPDA. For \(t\in[K']\), the parameters are \[ F'=\binom{K'}{t},\quad F=\binom{K}{t},\quad Z'=\binom{K'-1}{t-1},\quad Z=\binom{K-1}{t-1},\quad S=\binom{K'}{t+1}. \] This produces the hotplug memory-rate point \[ \left(\frac{M}{N},R\right)=\left(\frac{\binom{K-1}{t-1}}{\binom{K'}{t}},\frac{\binom{K'}{t+1}}{\binom{K'}{t}}\right) \] before repeated-demand reduction. The same paper observed that when \(Z>Z'\), the standard delivery transmits excess coded symbols per active user. By deleting a set of PDA labels \(T\) such that \(|T\cap C_i|\le Z-Z'\) in every column, it reduced the MAN-HpPDA rate to \[ \left( \frac{M}{N}, R \right) = \left( \frac{\binom{K-1}{t-1}}{\binom{K'}{t}}, \frac{\binom{K'}{t+1}-\left \lfloor \frac{K'}{t+1} \right \rfloor \left(\binom{K-1}{t-1}-\binom{K'-1}{t-1}\right)}{\binom{K'}{t}} \right). \] This is the first systematic rate-improvement mechanism internal to the HpPDA framework [2311.02856]. A second family constructs HpPDAs from \(t\)-designs. For a \(t\)-\((v,k,\lambda)\) design with point-incidence parameter \(\lambda_1\), choose integers \(a_s\in\{0,1,\dots,\lambda_s^t\}\), \(1\le s\le t-1\), and define \[ F'=\sum_{s=1}^{t-1} a_s\binom{t}{s},\qquad Z'=\sum_{s=1}^{t-1} a_s\binom{t-1}{s-1},\qquad S=\sum_{s=1}^{t-1} a_s\binom{t}{s+1}. \] The resulting \(t\)-scheme achieves \[ \left( \frac{M}{N}, R \right) = \left( \frac{\lambda_1}{\sum_{s=1}^{t-1} a_s \binom{t}{s}}, \frac{\sum_{s=1}^{t-1} a_s \binom{t}{s+1}}{\sum_{s=1}^{t-1} a_s \binom{t}{s}} \right), \] and the same label-deletion argument yields an improved rate \[ R= \frac{\sum_{s=1}^{t-1} a_s \binom{t}{s+1}-|T|} {\sum_{s=1}^{t-1} a_s \binom{t}{s}}. \] For \(K'=3\), the improved \(t\)-scheme reaches the cut-set line \(R=1-M/N\) at specific high-memory points arising from \(3\)-design families, and the paper shows that this optimal regime starts at a smaller memory ratio than the baseline hotplug scheme [2311.02856]. The MDS reuse of existing HpPDAs sharpened these tradeoffs further. For the \((8,3,8)\) hotplug system derived from a \(3\)-\((8,4,1)\) design, the new scheme in [2404.06433] turns two earlier HpPDAs into the points \((7/11,5/11)\) and \((7/13,8/13)\), and the paper reports that these points outperform the compared schemes in the memory range \(M\in(4.0975,5.4902)\). It also reports outperforming ranges \(M\in(5.1968,5.64103)\) for \((12,3,12)\) and \(M\in(5.9231,12)\) for \((12,5,12)\), while explicitly noting that the improvement comes with increased subpacketization [2404.06433]. ## 4. Shared caches, helper attachment, and topological generalizations Hotplug ideas also appear in shared-cache systems, where the uncertainty concerns attachment rather than merely activity. In the shared-cache model with private user caches, the network contains one server, \(K\) users, \(\Lambda\le K\) helper caches of size \(M_s\), and one private cache of size \(M_p\) per user. The hotplug-like case is the one in which the user-to-helper association is unknown during placement and revealed only before delivery. The proposed scheme splits each file into a helper-cache part of fraction \(f\) and a private-cache part of fraction \(1-f\), and achieves \[ R(M_s,M_p)=fR_s(t_s)+(1-f)R_p(t_p), \] with \[ t_s=\frac{\Lambda M_s}{fN},\qquad t_p=\frac{K M_p}{(1-f)N}. \] The helper and private components are placed independently, and the delivery is optimal for that placement via an index-coding converse. This captures late binding of users to helpers after prefetching, but it still assumes fixed \(K\), fixed \(\Lambda\), exactly one helper per user, centralized placement, and static attachment during delivery [2209.00299]. When the helper association is known in advance, the same paper shows that significantly stronger coupling is possible. Its joint shared-plus-private coding scheme achieves exact optimality in the regime \[ M_s \ge N\left(1-\frac{1}{\Lambda}\right), \qquad N \ge M_s+M_p \ge N\left(1-\frac{1}{\Lambda\mathcal L_1}\right), \] with \[ R^*(M_s,M_p)=1-\frac{M_s+M_p}{N}. \] This benchmark quantifies the price of not knowing the attachment structure during placement [2209.00299]. Two other topological extensions make hotplug behavior more structural. In shared-cache networks, generalized PDAs replicate cache columns according to the realized user-to-cache profile, so placement is association-oblivious and delivery adapts after association is revealed; this gives low-subpacketization schemes and recovers the optimal Parrinello–Ünsal–Elia shared-cache scheme as a special case when the starting PDA is the MAN PDA [2107.00361]. In a different direction, a matrix-and-design-based shared-cache scheme fixes subpacketization at \(q^m\), does not make it depend directly on the number of users or caches, and explicitly allows new caches to be added without redoing the placement of the existing caches, provided the enlarged matrix preserves the required circuit structure. This is a genuine cache-hotplug property, although delivery must still be recomputed for the expanded system [2212.14410]. Hierarchical and multi-access hotplug models extend the same principle to more complex topologies. HHPDA-based schemes handle two-layer networks with cache-aided mirrors and offline users, generalizing earlier work restricted to zero mirror memory [2507.00727]. Combinatorial multi-access hotplug networks allow each user to access an \(r\)-subset of \(C\) caches, declare a user active whenever \(U\cap I\neq\emptyset\) for the online-cache set \(I\), and use \(t\)-design-based generalized HpPDAs to obtain flexible rate-memory-subpacketization tradeoffs in which redundant multicast transmissions can be removed by parameter selection [2601.10503]. ## 5. Privacy, secrecy, and adaptive delivery Hotplug coded caching has also developed privacy-constrained variants. In **demand-private hotplug caching**, only \(K'\) users are active, but each active user requests a scalar linear combination of the \(N\) files, represented by a vector \(\mathbf d_j\in\mathbb F_q^N\). The privacy condition requires \[ I(\mathbf D_{\mathcal A\setminus\mathcal S}; X,\mathbf D_{\mathcal S}, Z_{\mathcal S}\mid F_{[N]})=0, \qquad \forall \mathcal S\subseteq\mathcal A,\ \mathcal S\neq\emptyset. \] Two MDS-based schemes are proposed. The first achieves \[ \left( M_t^{\rm(new)}, R_t^{\rm(new)} \right) = \left( \frac{\binom{K-1}{t-1}+ \left[\binom{K'}{t}- \binom{K-1}{t-1}\right]^+}{\binom{K'}{t}}, \frac{\binom{K'}{t+1} - \binom{K' - K''}{t+1}}{\binom{K'}{t}} \right), \] with subpacketization \(\binom{K'}{t}\), and matches the foresight benchmark in the small-memory regime \[ M\in\left[0,\ 1+\frac{N-1}{K'}\right]. \] A second scheme covers the large-memory endpoint \(M=N-(N-1)/K'\) with rate \(R=1/K'\) [2305.06518]. A stronger **secretive hotplug coded-caching** model requires both cache secrecy and delivery secrecy. Its conditions include \[ I(W_{[N]}; Z_k)=0,\qquad H(W_{d_k}\mid X,Z_k)=0,\qquad I(W_{[N]\setminus\{d_k\}}; X,Z_k)=0. \] For MAN-HpPDAs, the proposed secretive scheme achieves \[ (M,R)=\left( \frac{NZ+\binom{K-1}{t}}{F'-Z'}, \frac{S}{F'-Z'} \right), \] with the MAN-HpPDA parameters \(F=\binom{K}{t}\), \(F'=\binom{K'}{t}\), \(Z=\binom{K-1}{t-1}\), \(Z'=\binom{K'-1}{t-1}\), and \(S=\binom{K'}{t+1}\). In the special case \(t=K'-1\), it attains the secrecy lower bound \(R=1\) at \[ M=N\binom{K-1}{K'-2}. \] A second secretive construction based on \(t\)-design HpPDAs achieves \[ M= \frac{NZ}{F'-Z'} + \frac{1}{F'-Z'} \sum_{s=1}^{t-2} a_s\binom{K-1}{s}, \qquad R=\frac{S}{F'-Z'}, \] and both secretive schemes outperform a baseline adaptation of classical secretive PDA coding in certain memory regions [2507.13961]. A distinct but adjacent direction is adaptive delivery for arbitrary realized cache states. A deep reinforcement learning approach treats caches as arbitrary, uses a full cache/request state representation of dimension \(3NKF\), optimizes delivery only, and reports worst-case inference complexity \(\mathcal O(K^3F^2)\) versus SACM’s \(\mathcal O(K2^{2K})\). This is relevant to hotplug-like arbitrary side information at the start of delivery, but it does not model user join/leave during an episode and keeps \(K\) fixed [1912.04321]. ## 6. Dynamic interpretations, limitations, and open problems Two earlier dynamic lines of work clarify what hotplug coded caching does and does not include. Dynamic centralized coded caching across multiple rounds considers a persistent set of fixed users and a set of mobile users joining later, keeps the fixed users’ caches unchanged, fills only the new users’ caches, and then couples both groups through concatenating placement and saturating-matching delivery. For the \((K_1,K_2;M_1,M_2;N)\) model with \(t_i=K_iM_i/N\), it derives an achievable rate depending on whether \(M_1