arXiv subjects

Minquan Cheng

Publications and source records attributed to Minquan Cheng.

At least 19 recordsLinked to original sources

arXiv2026

Proactive Coded Caching Scheme for D2D Networks

Coded caching and device-to-device (D2D) communication are two effective techniques for alleviating network traffic. Secure transmission and file privacy have also become critical concerns in these domains. However, prevailing coded caching schemes typically assume that a user's cached content is inaccessible to others, overlooking the risk of file privacy leakage due to attacks targeting the cache itself. In this paper, we propose a secure coded caching scheme for D2D networks that guarantees both file privacy and secure delivery. We demonstrate that the proposed scheme achieves order-optimal performance when the file size is sufficiently large and the cache memory is ample.

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arXiv2026

A Low-Complexity Framework for Multi-access Coded Caching Systems with Arbitrary User-cache Access Topology

This paper studies the multi-access coded caching (MACC) problem with arbitrary user-cache access topology, which extends existing MACC models that rely on highly structured and combinatorially designed topologies. We consider a MACC system consisting of a single server, $\Lambda$ cache-nodes, and $K$ user-nodes. The server stores $N$ equal-size files, each cache-node has a storage capacity of $M$ files, and each user-node $k\in[K]$ can access an arbitrary subset of cache-nodes $\mathcal{A}_k\subseteq[\Lambda]$ and retrieve the cached content stored in cache-nodes $\mathcal{A}_k$. The objective is to design a universal framework for the MACC delivery problem. Decoding conflicts among the requested packets are captured by a conflict graph, and the design of the delivery is reduced to a graph coloring problem, where achieving a lower transmission load corresponds to coloring the graph using fewer colors. Under this formulation, the classical DSatur algorithm achieves a transmission load close to the index-coding (IC) converse bound, thereby providing a practical benchmark. However, its computational complexity becomes prohibitive for large-scale graphs. To overcome this limitation, we develop a learning-driven approach using graph neural networks (GNNs) that efficiently constructs coded multicast transmissions with performance close to the theoretical bounds and generalizes across different user-cache access topologies and numbers of users. In addition, we extend the IC converse bound to MACC systems with arbitrary access topology and propose a low-complexity greedy approximation that closely matches the IC converse bound. Numerical results demonstrate that the proposed approach achieves performance close to the DSatur algorithm and the IC converse bound, while significantly reducing computational complexity, making it well-suited for large-scale MACC systems.

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arXiv2026

Distributed Linearly Separable Computation with Arbitrary Heterogeneous Data Assignment

Distributed linearly separable computation is a fundamental problem in large-scale distributed systems, requiring the computation of linearly separable functions over different datasets across distributed workers. This paper studies a heterogeneous distributed linearly separable computation problem, including one master and N distributed workers. The linearly separable task function involves Kc linear combinations of K messages, where each message is a function of one dataset. Distinguished from the existing homogeneous settings that assume each worker holds the same number of datasets, where the data assignment is carefully designed and controlled by the data center (e.g., the cyclic assignment), we consider a more general setting with arbitrary heterogeneous data assignment across workers, where `arbitrary' means that the data assignment is given in advance and `heterogeneous' means that the workers may hold different numbers of datasets. Our objective is to characterize the fundamental tradeoff between the computable dimension of the task function and the communication cost under arbitrary heterogeneous data assignment. Under the constraint of integer communication costs, for arbitrary heterogeneous data assignment, we propose a universal computing scheme and a universal converse bound by characterizing the structure of data assignment, where they coincide under some parameter regimes. We then extend the proposed computing scheme and converse bound to the case of fractional communication costs.

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arXiv2026

A New Construction Structure on MISO Coded Caching with Linear Subpacketization: Half-Sum Disjoint Packing

In the $(L,K,M,N)$ cache-aided multiple-input single-output (MISO) broadcast channel (BC) system, the server is equipped with $L$ antennas and communicates with $K$ single-antenna users through a wireless broadcast channel where the server has a library containing $N$ files, and each user is equipped with a cache of size $M$ files. Under the constraints of uncoded placement and one-shot linear delivery strategies, many schemes achieve the maximum sum Degree-of-Freedom (sum-DoF). However, for general parameters $L$, $M$, and $N$, their subpacketizations increase exponentially with the number of users. We aim to design a MISO coded caching scheme that achieves a large sum-DoF with low subpacketization $F$. An interesting combinatorial structure, called the multiple-antenna placement delivery array (MAPDA), can be used to generate MISO coded caching schemes under these two strategies; moreover, all existing schemes with these strategies can be represented by the corresponding MAPDAs. In this paper, we study the case with $F=K$ (i.e., $F$ grows linearly with $K$) by investigating MAPDAs. Specifically, based on the framework of Latin squares, we transform the design of MAPDA with $F=K$ into the construction of a combinatorial structure called the $L$-half-sum disjoint packing (HSDP). It is worth noting that a $1$-HSDP is exactly the concept of NHSDP, which is used to generate the shared-link coded caching scheme with $F=K$. By constructing $L$-HSDPs, we obtain a class of new schemes with $F=K$. Finally, theoretical and numerical analyses show that our $L$-HSDP schemes significantly reduce subpacketization compared to existing schemes with exponential subpacketization, while only slightly sacrificing sum-DoF, and achieve both a higher sum-DoF and lower subpacketization than the existing schemes with linear subpacketization.

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arXiv2026

Multiaccess Coded Caching with Heterogeneous Retrieval Costs

The multiaccess coded caching (MACC) system, as formulated by Hachem {\it et al.}, consists of a central server with a library of $N$ files, connected to $K$ cache-less users via an error-free shared link, and $K$ cache nodes, each equipped with cache memory of size $M$ files. Each user can access $L$ neighboring cache nodes under a cyclic wrap-around topology. Most existing studies operate under the strong assumption that users can retrieve content from their connected cache nodes at no communication cost. In practice, each user retrieves content from its $L$ different connected cache nodes at varying costs. Additionally, the server also incurs certain costs to transmit the content to the users. In this paper, we focus on a cost-aware MACC system and aim to minimize the total system cost, which includes cache-access costs and broadcast costs. Firstly, we propose a novel coded caching framework based on superposition coding, where the MACC schemes of Cheng \textit{et al.} are layered. Then, a cost-aware optimization problem is derived that optimizes cache placement and minimizes system cost. By identifying a sparsity property of the optimal solution, we propose a structure-aware algorithm with reduced complexity. Simulation results demonstrate that our proposed scheme consistently outperforms the scheme of Cheng {\it et al.} in scenarios with heterogeneous retrieval costs.

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arXiv2026

Placement Delivery Array for Cache-Aided MIMO Systems

We consider a $(G,L,K,M,N)$ cache-aided multiple-input multiple-output (MIMO) network, where a server equipped with $L$ antennas and a library of $N$ equal-size files communicates with $K$ users, each equipped with $G$ antennas and a cache of size $M$ files, over a wireless interference channel. Each user requests an arbitrary file from the library. The goal is to design coded caching schemes that simultaneously achieve the maximum sum degrees of freedom (sum-DoF) and low subpacketization. In this paper, we first introduce a unified combinatorial structure, termed the MIMO placement delivery array (MIMO-PDA), which characterizes uncoded placement and one-shot zero-forcing delivery. By analyzing the combinatorial properties of MIMO-PDAs, we derive a sum-DoF upper bound of $\min\{KG, Gt+G\lceil L/G \rceil\}$, where $t=KM/N$, which coincides with the optimal DoF characterization in prior work by Tehrani \emph{et al.}. Based on this upper bound, we present two novel constructions of MIMO-PDAs that achieve the maximum sum-DoF. The first construction achieves linear subpacketization under stringent parameter constraints, while the second achieves ordered exponential subpacketization under substantially milder constraints. Theoretical analysis and numerical comparisons demonstrate that the second construction exponentially reduces subpacketization compared to existing schemes while preserving the maximum sum-DoF.

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arXiv2026

A Construction Framework of Coded Caching Scheme for Multi-Access MISO Systems via Knapsack Problem

This paper investigates the coded caching problem in a multi-access multiple-input single-output (MAMISO) network with the combinatorial topology. The considered system consists of a server containing $N$ files, $\Lambda$ cache nodes, and $K$ cache-less users, where each user can access a unique subset of $r$ cache nodes. The server is equipped with $L$ transmit antennas. Our objective is to design a caching scheme that simultaneously achieves a high sum Degree of Freedom (sum-DoF) and low subpacketization complexity. To address this challenge, we formulate the design of multi-antenna placement delivery arrays (MAPDA) as a $0$--$1$ knapsack problem to maximize the achievable DoF, thereby transforming the complex combinatorial caching structure into a tractable optimization framework that yields efficient cache placement and flexible delivery strategies. Theoretical and numerical analyses demonstrate that: for networks with combinatorial topologies, the proposed scheme achieves a higher sum-DoF than existing schemes. Under identical cache size constraints, the subpacketization level remains comparable to existing linear subpacketization schemes. Moreover, under specific system conditions, the proposed scheme attains the theoretical maximum sum-DoF of $\min\{L+KM/N, K\}$ while achieving further reductions subpacketization. For particular combinatorial structures, we further derive optimized constructions that achieve even higher sum-DoF with lower subpacketization. ```

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arXiv2026

A New Construction Structure on Coded Caching with Linear Subpacketization: Non-Half-Sum Latin Rectangle

Coded caching is recognized as an effective method for alleviating network congestion during peak periods by leveraging local caching and coded multicasting gains. The key challenge in designing coded caching schemes lies in simultaneously achieving low subpacketization and low transmission load. Most existing schemes require exponential or polynomial subpacketization levels, while some linear subpacketization schemes often result in excessive transmission load. Recently, Cheng et al. proposed a construction framework for linear coded caching schemes called Non-Half-Sum Disjoint Packing (NHSDP), where the subpacketization equals the number of users $K$. This paper introduces a novel combinatorial structure, termed the Non-Half-Sum Latin Rectangle (NHSLR), which extends the framework of linear coded caching schemes from $F=K$ (i.e., the construction via NHSDP) to a broader scenario with $F=\mathcal{O}(K)$. By constructing NHSLR, we have obtained a new class of coded caching schemes that achieves linearly scalable subpacketization, while further reducing the transmission load compared with the NHSDP scheme. Theoretical and numerical analyses demonstrate that the proposed schemes not only achieves lower transmission load than existing linear subpacketization schemes but also approaches the performance of certain exponential subpacketization schemes.

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arXiv2026

A New Construction Structure on Multi-access Coded Caching with Linear Subpacketization: Cyclic Multi-Access Non-Half-Sum Disjoint Packing

We consider the $(K,L,M,N)$ multi-access coded caching system introduced by Hachem et al., which consists of a central server with $N$ files and $K$ cache nodes, each of memory size $M$, where each user can access $L$ cache nodes in a cyclic wrap-around fashion. At present, several existing schemes achieve competitive transmission performance, but their subpacketization levels grow exponentially with the number of users. In contrast, schemes with linear or polynomial subpacketization always incur higher transmission loads. We aim to design a multi-access coded caching scheme with linear subpacketization $F$ while maintaining low transmission load. Recently, Cheng et al. proposed a construction framework for coded caching schemes with linear subpacketization (i.e., $F=K$) called non-half-sum disjoint packing (NHSDP). Inspired by this structure, we introduce a novel combinatorial structure named cyclic multi-access non-half-sum disjoint packing (CMA-NHSDP) by extending NHSDP to MACC system. By constructing CMA-NHSDP, we obtain a new class of multi-access coded caching schemes. Theoretical and numerical analyses show that our scheme achieves lower transmission loads than some existing schemes with linear subpacketization. Moreover, the proposed schemes achieves lower transmission load compared to existing schemes with exponential subpacketization in some case.

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arXiv2025

Entropy Functions on Two-Dimensional Faces of Polymatroidal Region of Degree Four: Part II: Information Theoretic Constraints Breed New Combinatorial Structures

Characterization of entropy functions is of fundamental importance in information theory. By imposing constraints on their Shannon outer bound, i.e., the polymatroidal region, one obtains the faces of the region and entropy functions on them with special structures. In this series of two papers, we characterize entropy functions on the $2$-dimensional faces of the polymatroidal region $\Gamma_4$. In Part I, we formulated the problem, enumerated all $59$ types of $2$-dimensional faces of $\Gamma_4$ by a algorithm, and fully characterized entropy functions on $49$ types of them. In this paper, i.e., Part II, we will characterize entropy functions on the remaining $10$ types of faces, among which $8$ types are fully characterized and $2$ types are partially characterized. To characterize these types of faces, we introduce some new combinatorial design structures which are interesting in themselves.

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arXiv2025

Fundamental Limits of Coded Caching with Fixed Subpacketization

Coded caching is a promising technique to create coded multicast opportunities for cache-aided networks. By splitting each file into $F$ equal packets (i.e., the subpacketization level $F$) and letting each user cache a set of packets, the transmission load can be significantly reduced via coded multicasting. It has been shown that a higher subpacketization level could potentially lead to a lower transmission load, as more packets can be combined for efficient transmission. On the other hand, a larger $F$ indicates a higher coding complexity and is problematic from a practical perspective when $F$ is extremely large. Despite many works attempting to design coded caching schemes with low subpacketization levels, a fundamental problem remains open: What is the minimum transmission load given any fixed subpacketization level? In this paper, we consider the classical cache-aided networks with identically uncoded placement and one-shot delivery strategy, and investigate the fundamental trade-off between the transmission load and the subpacketization level. We propose a \emph{general} lower bound on the transmission load for any fixed subpacketization by reformulating the centralized coded caching schemes via the combinatorial structure of the corresponding placement delivery array. The lower bound also recovers existing optimality results for the bipartite graph scheme (including the well-known Maddah-Ali and Niesen (MN) scheme and the conjugate MN scheme) as well as the grouping bipartite graph scheme. Furthermore, by carefully exploiting the combinatorial structure and computing the union size of sorted sets, we establish a new optimality result, i.e., the partition scheme can achieve the optimal rate-subpacketization trade-off.

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arXiv2025

On Anti-collusion Codes for Averaging Attack in Multimedia Fingerprinting

Multimedia fingerprinting is a technique to protect the copyrighted contents against being illegally redistributed under various collusion attack models. Averaging attack is the most fair choice for each colluder to avoid detection, and also makes the pirate copy have better perceptional quality. This makes such an attack one of the most feasible approaches to carrying out collusion. In order to trace all the colluders, several types of multimedia fingerprinting codes were introduced to construct fingerprints resistant to averaging attacks on multimedia contents, such as AND anti-collusion codes (AND-ACCs), binary separable codes (SCs), logical anti-collusion codes (LACCs), binary frameproof codes (FPCs), binary strongly-separable codes (SSCs) and binary secure code with list decoding (SCLDs). Then codes with the rate as high as possible are desired. However, the existing fingerprinting codes have low code rate due to the strong combinatorial structure. The reason is that the previous research methods adopted simple tracing algorithms. In this paper, we first propose novel tracing algorithms and then find appropriate fingerprinting codes with weaker combinatorial structure, i.e., the binary strongly identifiable parent property code for multimedia fingerprinting (SMIPPC) and its concatenated code. Theoretical comparisons and numerical comparisons show that SMIPPCs have higher code rates than those of the existing codes due to their weaker combinatorial structures. It is worth noting that SMIPPCs can only trace a part of colluders by using the previous tracing algorithm and the concatenated SMIPPC may be not an SMIPPC. This implies that our tracing algorithms have strong traceability.

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arXiv2025

A Novel Coded Computing Approach for Distributed Multi-Task Learning

Distributed multi-task learning (DMTL) effectively improves model generalization performance through the collaborative training of multiple related models. However, in large-scale learning scenarios, communication bottlenecks severely limit practical system performance. In this paper, we investigate the communication bottleneck within a typical DMTL system that employs non-linear global updates. This system involves distributed workers, assisted by a central server, who collaboratively learn distinct models derived from a non-linear aggregation of their local model parameters. We first characterize the communication process as a matrix decomposition problem. It transforms workers' data storage constraints into structural characteristics of the uplink encoding matrix, and worker data retrieval demands into Maximum Distance Separable (MDS) properties of the downlink encoding matrix. Building on this, we propose a novel coded DTML scheme that can greatly reduce the communication cost of the DTML with heterogeneous data placement. Theoretical analysis demonstrates that the proposed scheme achieves the theoretical lower bound for communication overhead under mild conditions. Remarkably, this optimality holds for both traditional homogeneous computing environments and various heterogeneous scenarios. Furthermore, our scheme is extensible to a distributed linearly separable computation problem where the target function involves multiple linear combinations of local update values. This indicates that our scheme offers a new way of tackling heterogeneous data placement challenges in various distributed applications.

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arXiv2025

On the Optimality of Coded Distributed Computing for Ring Networks

We consider a coded distributed computing problem in a ring-based communication network, where $N$ computing nodes are arranged in a ring topology and each node can only communicate with its neighbors within a constant distance $d$. To mitigate the communication bottleneck in exchanging intermediate values, we propose new coded distributed computing schemes for the ring-based network that exploit both ring topology and redundant computation (i.e., each map function is computed by $r$ nodes). Two typical cases are considered: all-gather where each node requires all intermediate values mapped from all input files, and all-to-all where each node requires a distinct set of intermediate values from other nodes. For the all-gather case, we propose a new coded scheme based on successive reverse carpooling where nodes transmit every encoded packet containing two messages traveling in opposite directions along the same path. Theoretical converse proof shows that our scheme achieves the optimal tradeoff between communication load, computation load $r$, and broadcast distance $d$ when $N\gg d$. For the all-to-all case, instead of simply repeating our all-gather scheme, we delicately deliver intermediate values based on their proximity to intended nodes to reduce unnecessary transmissions. We derive an information-theoretic lower bound on the optimal communication load and show that our scheme is asymptotically optimal under the cyclic placement when $N\gg r$. The optimality results indicate that in ring-based networks, the redundant computation $r$ only leads to an additive gain in reducing communication load while the broadcast distance $d$ contributes to a multiplicative gain.

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arXiv2025

Rack-Aware MSR Codes with Linear Field Size and Smaller Sub-Packetization for Tolerating Multiple Erasures

In an $(n,k,d)$ rack-aware storage model, the system consists of $n$ nodes uniformly distributed across $\bar{n}$ successive racks, such that each rack contains $u$ nodes of equal capacity and the reconstructive degree satisfies $k=\bar{k}u+v$ where $0\leq v\leq u-1$. Suppose there are $h\geq1$ failed nodes in a rack (called the host rack). Then together with its surviving nodes, the host rack downloads recovery data from $\bar{d}$ helper racks and repairs its failed nodes. In this paper, we focus on studying the rack-aware minimum storage generating (MSR) codes for repairing $h$ failed nodes within the same rack. By using the coupled-layer construction with the alignment technique, we construct the first class of rack-aware MSR codes for all $\bar{k}+1\leq\bar{d}\leq\bar{n}-1$ which achieve the small sub-packetization $l=\bar{s}^{\lceil\bar{n}/\bar{s}\rceil}$ where the field size $q$ increases linearly with $n$ and $\bar{s}=\bar{d}-\bar{k}+1$. In addition, these codes achieve optimal repair bandwidth for $1\leq h\leq u-v$, and asymptotically optimal repair bandwidth for $u-v+1\leq h\leq u$. In particular, they achieve optimal access when $h=u-v$. It is worth noting that the existing rack-aware MSR codes which achieve the same sub-packetization $l=\bar{s}^{\lceil\bar{n}/\bar{s}\rceil}$ are only known for the special case of $\bar{d}=\bar{n}-1$, $h=1$, and the field size is much larger than ours. Then, based on our first construction we further develop another class of explicit rack-aware MSR codes with even smaller sub-packetization $l=\bar{s}^{\lceil\bar{n}/(\bar{s}+1)\rceil}$ for all admissible values of $\bar{d}$.

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arXiv2025

Explicit Constructions for Rack-Aware Minimum Storage Partially Cooperative Regenerating Codes

The rack-aware storage model improves repair efficiency by exploiting locality within racks to minimize cross-rack traffic in a distributed storage system. While the partially cooperative repair model presents a solution for multiple node failures that reduces the need to exchange data with all other host racks (defined as racks containing failed nodes), thus enhancing system flexibility. In this paper, we focus on rack-aware minimum storage partially cooperative regenerating (MSPCR) codes for repairing multiple node failures. We first derive the lower bound on the repair bandwidth for rack-aware MSPCR codes using extremal combinatorics, and then explicitly construct the first class of (asymptotically) optimal repair schemes for rack-aware MSPCR codes with a sub-packetization level of $(\bar{s}+\bar{h}-\delta)\bar{s}^{\bar{n}}$, which is smaller than that of the known rack-aware minimum-storage cooperative regenerating (MSCR) codes when $\delta \geq 2$. By utilizing the grouping technique, we explicitly construct the second class of (asymptotically) optimal repair schemes for rack-aware MSPCR codes with a sub-packetization level of $2^{\bar{n}}$. In particular, when $\delta=1$, our second codes reduce to rack-aware MSCR codes, while achieving an $(\bar{h}+1)$-fold reduction in sub-packetization level compared to the known rack-aware MSCR codes.

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arXiv2025

PDA Construction via Union of Cartesian Product Cache Configurations for Coded Caching

Caching is an efficient technique to reduce peak traffic by storing popular content in local caches. Placement delivery array (PDA) proposed by Yan et al. is a combinatorial structure to design coded caching schemes with uncoded placement and one-shot linear delivery. By taking the $m$-fold Cartesian product of a small base PDA, Wang et al. constructed a big PDA while maintaining the memory ratio and transmission load unchanged, which achieves linear growth in both the number of users and coded caching gain. In order to achieve exponential growth in both the number of users and coded caching gain, in this paper we propose a PDA construction by taking the union operation of the cache configurations from the $m$-fold Cartesian product of a base PDA. The resulting PDA leads to a coded caching scheme with subpacketization increasing sub-exponentially with the number of users while keeping the load constant for fixed memory ratio. By applying the proposed construction to existing base PDAs, three new coded caching schemes are obtained, which cover some existing schemes as special cases and can achieve lower load with simultaneously lower subpacketization for some memory ratios.

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arXiv2025

A New Construction Structure on Coded Caching with Linear Subpacketization: Non-Half-Sum Disjoint Packing

Coded caching is a promising technique to effectively reduce peak traffic by using local caches and the multicast gains generated by these local caches. We prefer to design a coded caching scheme with the subpacketization $F$ and transmission load $R$ as small as possible since these are the key metrics for evaluating the implementation complexity and transmission efficiency of the scheme, respectively. However, most of the existing coded caching schemes have large subpacketizations which grow exponentially with the number of users $K$, and there are a few schemes with linear subpacketizations which have large transmission loads. In this paper, we focus on studying the linear subpacketization, i.e., $K=F$, coded caching scheme with low transmission load. Specifically, we first introduce a new combinatorial structure called non-half-sum disjoint packing (NHSDP) which can be used to generate a coded caching scheme with $K=F$. Then a class of new schemes is obtained by constructing NHSDP. Theoretical and numerical comparisons show that (i) compared to the existing schemes with linear subpacketization (to the number of users), the proposed scheme achieves a lower load; (ii) compared to some existing schemes with polynomial subpacketization, the proposed scheme can also achieve a lower load in some cases; (iii) compared to some existing schemes with exponential subpacketization, the proposed scheme has loads close to those of these schemes in some cases. Moreover, the new concept of NHSDP is closely related to the classical combinatorial structures such as cyclic difference packing (CDP), non-three-term arithmetic progressions (NTAP), and perfect hash family (PHF). These connections indicate that NHSDP is an important combinatorial structure in the field of combinatorial design.

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