Multi-Access Coded Caching (MACC)

• Multi-Access Coded Caching (MACC) is a framework with models, algorithms, and results for distributed caching where users access multiple caches.
• It examines various topologies—cyclic, combinatorial, arbitrary—and employs both uncoded and coded placement to balance subpacketization and delivery rates.
• MACC offers practical insights on optimizing memory-rate trade-offs and coding gains, with approaches extending to multi-antenna, secure, and D2D networks.

Multi-Access Coded Caching (MACC) refers to a family of information-theoretic models, algorithms, and achievability/optimality results for distributed caching networks in which each user has simultaneous access to the contents of multiple caches. Unlike classical shared-link coded caching—where each user holds a dedicated cache—MACC introduces richer, potentially cyclic or combinatorial cache-user connectivity, leading to fundamentally different placement and delivery strategies, coding gains, and trade-offs between subpacketization, delivery rate, and network structure.

1. System Model Variants

The essential structure of MACC encompasses a data server holding a library of $N$ files, $K$ users, $K$ (or more generally $\Lambda$) cache nodes (helpers), and a shared error-free broadcast link for delivery. Each user connects to a specific subset of caches, from which it can retrieve content at zero or nonzero cost, and possibly holds a local (private) cache as well. The access pattern is a key modeling choice:

• Cyclic Wrap-Around Topology: Each user accesses $L$ consecutive caches arranged in a ring topology, as in the “HKD” (Hachem-Karamchandani-Diggavi) model (Cheng et al., 2020, Namboodiri et al., 2022).
• Combinatorial Topology: Each user is associated with a fixed-size subset (e.g., an $r$-subset) of all caches, potentially achieving exponential scaling in user count $K$ with respect to $\Lambda$ (Brunero et al., 2021, Cheng et al., 2023, Singh et al., 2024).
• Arbitrary Topology: General setting where user-to-cache connectivity is specified by a bipartite graph, allowing arbitrary associations (Yang et al., 15 Jan 2026, Das et al., 2022).
• Private+Access Caches: Settings where users have both private and multi-access memory, leading to augmented coding opportunities (Singh et al., 2024, Singh et al., 2024).

The MACC framework also extends to two-dimensional grid-based topologies, multi-antenna wireless networks, device-to-device (D2D) variants, and cost-aware or secure delivery models (Zhang et al., 2022, Namboodiri et al., 2024, Peter et al., 2023, Huang et al., 15 Jan 2026, Namboodiri et al., 2021).

2. Placement and Delivery Schemes

The operation splits into two classes of schemes distinguished by their approach to cache placement and coded delivery:

• Uncoded Placement Schemes: Files are partitioned into subfiles and assigned to caches using cyclic, combinatorial, or graph-based rules. Delivery exploits coded multicasting, such as XOR'ing requested subfile indices across users with overlapping cache coverage, following variants of Maddah-Ali/Niesen (MAN) schemes generalized to multi-access patterns (Cheng et al., 2020, Namboodiri et al., 2022, Singh et al., 2024, Brunero et al., 2021).
• Coded Placement and Combinatorial Design: More generally, placement and delivery can be specified via combinatorial structures such as resolvable designs, maximal cross-resolvable designs, $t$-designs, group-divisible designs, or placement-delivery arrays (PDAs), enabling finer trade-offs between subpacketization and transmission rate (Das et al., 2022, Cheng et al., 2023, Katyal et al., 2020).
• Linear Subpacketization: Recent works address the exponential increase in subpacketization with $K$ by constructing schemes with $F=O(K)$ (linear) or low polynomial $F$ at moderate rate penalty, leveraging PDA structures, index coding reductions, or non-half-sum disjoint packing (Kota et al., 2023, Sasi et al., 2021, Wang et al., 2022, Li et al., 15 Jan 2026).
• Multicast Message Compression and Superposition: Further improvements in delivery rate are achieved by compressing redundant transmissions (identifying “null” multicasts from local cache coverage) or layering multiple access-level schemes to optimize delivery cost under heterogeneous retrieval costs (Cheng et al., 2020, Huang et al., 15 Jan 2026).

See the following representative table for some canonical system configurations, as realized in recent MACC literature:

Topology	Placement Type	Subpacketization	Achieved Rate Expression	Reference
Cyclic wrap-around	Uncoded, PDA	$F=\binom{K}{t}$, $F=K$ (linear)	$R=(K-tL)/(t+1)$, $R = (K-iL)(K-iL+1)/2K$, etc.	(Cheng et al., 2020, Wang et al., 2022, Kota et al., 2023)
Combinatorial ($r$-subset)	Uncoded (MAN-style)	$F = \binom{C}{t}$	$R = \binom{C}{t+r} / \binom{C}{t}$	(Brunero et al., 2021, Singh et al., 2024)
Arbitrary bipartite	Uncoded (MN)	$F = \binom{\Lambda}{t}$	$R$ via conflict graph coloring, index coding	(Yang et al., 15 Jan 2026, Das et al., 2022)
2D grid	Uncoded / PDA	$F$ depends on grouping/projection	$R = (K_1K_2 - tL^2)/(t+1)$, others	(Zhang et al., 2022, Namboodiri et al., 2024)

3. Achievability Results and Information-Theoretic Bounds

Analytic progress relies on several tightly coupled components:

• MAN-style Achievability: In the combinatorial (uniform $r$-subset) access topology, there exists an uncoded-placement-and-MAN-delivery scheme that is exactly optimal for worst-case delivery rate at memory points $M = N t / \Lambda$, rate $R^*(M) = \binom{\Lambda}{r+t} / \binom{\Lambda}{t}$, and $K=\binom{\Lambda}{r}$ (Brunero et al., 2021). The proof uses index coding and the acyclic subgraph bound.
• Cyclic Wrap-Around Achievability: For the wrap-around model, the transformed MAN construction achieves $F=K\binom{K-t(L-1)}{t}$, rate $R=(K-tL)/(t+1)$ at $M=t N/K$ (Cheng et al., 2020). Compression and refinements allow further reduction of delivery rate by eliminating redundant transmissions.
• Lower Bounds (Converse): Cut-set-based lower bounds generalize to the multi-access setting as $$R^*(M) \ge \max_{s}\{s - (p M)/\lfloor N/s \rfloor \}$$, $p=\min\{s+L-1,K\}$; stronger bounds leverage entropy inequalities (sliding-window/intersecting sets) for tighter analysis (Namboodiri et al., 2022, Singh et al., 2024). In the combinatorial topology, optimality of uncoded placement is provable (Brunero et al., 2021).
• Linear Subpacketization and Rate Penalty: Achievability with $F=O(K)$ is established at moderately higher $R$ (explicit expressions via index coding), and for certain parameter regimes matches or strictly outperforms prior exponential-$F$ constructions (Sasi et al., 2021, Kota et al., 2023, Wang et al., 2022, Li et al., 15 Jan 2026).
• Large Memory Regime: In both cyclic and combinatorial settings, once the sum "accessed memory" per user $M_A L + M_P$ or $r M_A + M_P$ exceeds $N(1-1/K)$, the scheme achieves the cut-set bound exactly, and the delivery rate saturates the information-theoretic minimum $R^*=1/K$ (Singh et al., 2024).

4. Topological Generalizations and Design Trade-offs

MACC provides a flexible methodological framework for varying user-cache incidence structures:

• Connectivity-Topology-Performance Trade-offs: Topologies derived from $t$-designs, group-divisible designs, cross-resolvable designs, or arbitrary bipartite graphs can interpolate between linear, polynomial, or exponential scaling in $K$ for a given $\Lambda$, affecting both subpacketization and achievable multicast gains (Das et al., 2022, Cheng et al., 2023, Katyal et al., 2020).
• Flexibility in Coding Gain: For fixed $K$, $L$, schemes based on combinatorial design allow fine-tuned control of coded multicasting gain and memory-rate profile through selection of the $t$ parameter in the design, or block sizes in resolvable or cross-resolvable designs.
• Support for Arbitrary User Numbers: MACC schemes with designs or combinatorial structures overcome the restriction of $K$ scaling rigidly with $\Lambda$ as in cyclic models, providing broader applicability for networks with heterogeneous or non-uniform topologies (Cheng et al., 2023).
• Cost-Aware and Heterogeneous Models: Recent models introduce retrieval cost heterogeneity across user-cache links, leading to superposition-based schemes and optimization problems that balance broadcast vs. retrieval costs, with provable sparsity properties in optimal allocations (Huang et al., 15 Jan 2026).

5. Extensions: Multi-Antenna, 2D Topology, Security, and D2D

MACC theory and practice extend in several important directions:

• Multi-Antenna and 2D MACC: Array-based construction principles allow extension to wireless systems with multiple transmit antennas (MISO BC), yielding delivery time (NDT) formulas with spatial multiplexing gains. 2D topologies with users and caches on rectangular grids attain new levels of locality and global gain (Peter et al., 2023, Namboodiri et al., 2024, Zhang et al., 2022).
• Secure Coded MACC: MACC with secure delivery against external eavesdroppers requires cache-aided key placement (e.g., via AIR matrices, one-time pad splitting) and achieves provably constant-factor optimal rates under perfect secrecy constraints (Namboodiri et al., 2021).
• Device-to-Device (D2D) MACC: Extension to D2D networks with multi-access-relay structure leverages similar combinatorial and design-based approaches for constructing low subpacketization, high gain D2D coded caching schemes (T. et al., 18 Jan 2025).

6. Computational and Practical Aspects

• Delivery Design with Arbitrary Topology: For general (non-structured) user-cache graphs, the delivery construction can be framed as a graph coloring problem on the conflict graph derived from cache-retrieval capabilities. Greedy (DSatur), GNN-based, and index coding lower bounds provide scalable solutions and tight performance for large, irregular topologies (Yang et al., 15 Jan 2026).
• Subpacketization Complexity: Except for recent linear-$F$ schemes, most high-rate MACC constructions suffer from impractically large subpacketization. Combinatorial and PDA-based solutions seek balance, and construction via maximal cross-resolvable designs or cyclic non-half-sum disjoint packings provides further explicit low-$F$ families (Das et al., 2022, Li et al., 15 Jan 2026).
• Superposition and Sparsity: Cost-aware MACC optimization is tractable due to the two-point sparsity of superposition solutions, making practical deployment realistic even for complex cost structures (Huang et al., 15 Jan 2026).

7. Connections to Broader Literature and Open Directions

MACC provides a unifying abstraction for numerous coded caching models, including: dedicated-cache MAN, cyclic wrap-around (HKD), combinatorial MACC, PDA/DPDA frameworks, t-design and group-divisible design-based schemes, arbitrary bipartite topologies, and grid-based or spatially-aware deployments. Several research challenges remain open:

• Tight information-theoretic converses for coded placement in multi-access topologies.
• General optimality criteria for nonuniform or time-varying topologies.
• Extension to asynchrony, demand heterogeneity, and decentralized placement.
• Subpacketization/rate trade-off optimization via new combinatorial or algebraic structures.

MACC thus constitutes a broad, technically rich field linking combinatorial design, network information theory, distributed algorithms, and practical system architecture for next-generation cache-aided networks (Cheng et al., 2020, Brunero et al., 2021, Cheng et al., 2023, Singh et al., 2024, Kota et al., 2023, Wang et al., 2022, Zhang et al., 2022, Yang et al., 15 Jan 2026, Li et al., 15 Jan 2026, Singh et al., 2024).