arXiv subjects

Minquan Cheng

Publications and source records attributed to Minquan Cheng.

At least 37 records · Page 2Linked to original sources

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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arXiv2025

Order Optimal Cascaded Code Distributed Computing With Low Complexity and Improved Flexibility

Coded distributed computing (CDC), proposed by Li \emph{et al.}, offers significant potential for reducing the communication load in MapReduce computing systems. In cascaded CDC with $K$ nodes, $N$ input files, and $Q$ output functions, each input file will be mapped by $r\geq 1$ nodes and each output function will be computed by $s>1$ nodes such that coding techniques can be applied to generate multicast opportunities. However, a significant limitation of most existing coded distributed computing schemes is their requirement to split the original data into a large number of input files (or output functions) that grows exponentially with $K$, which significantly increases the coding complexity and degrades the system performance. In this paper, we focus on the case of $K/s\in\mathbb{N}$, deliberately designing the strategy of data placement and output functions assignment, such that a low-complexity CDC scheme is achievable. The main advantages of the proposed scheme include: 1) the multicast gains equal to $(r+s-1)(1-1/s)$ and $r+s-1$ which is approximately $r+s-1$ when $s$ is relatively large, and the communication load potentially better than the well-known scheme proposed by Li \emph{et al.}; 2) the proposed scheme requires significantly less input files and output functions; 3) all the operations are implemented over the binary field $\mathbb{F}_2$ with the one-shot fashion (i.e., each node can decode its requested content immediately upon receiving the multicast message during the current time slot). Finally, we derive a new information-theoretic converse bound for the cascaded CDC framework under the proposed strategies of data placement and output functions assignment. We demonstrate that the communication load of the proposed scheme is order optimal within a factor of $2$; and is also approximately optimal when $K$ is sufficiently large for a given $r$.

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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

Improved Coded Caching Scheme for Multi-User Information Retrieval System

In this paper, we study the coded caching scheme for the $(L, K, M, N)$ multi-user information retrieval (MIR) system, which consists of a content library containing $N$ files, a base station (BS) with $L$ antennas that cannot access the library, and $K$ single-antenna users, each of which can cache at most $M$ files from the library. The users communicate with the others assisted by the BS to decode their required files. In this paper, we focus on designing a coded caching scheme with low communication latency measured by normalized delivery time (NDT), computational complexity, and subpacketizations. When $\frac{KM}{N}\geq L$ we first simply the precoding matrix in the downlink step to an identity matrix and use the multiple-antenna placement delivery array (MAPDA), which was originally proposed for the multiple-input single-output networks, to generate several new schemes for MIR system. Compared to the existing schemes, both the theoretical and numerical analyses show that our new schemes achieve much lower computational complexity and smaller subpacketizations with the same NDT.

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arXiv2024

Matroidal Entropy Functions: Constructions, Characterizations and Representations

Matroidal entropy functions are entropy functions in the form $\mathbf{h} = \log v \cdot \mathbf{r}_M$ , where $v \ge 2$ is an integer and $\mathbf{r}_M$ is the rank function of a matroid $M$. They can be applied into capacity characterization and code construction of information theory problems such as network coding, secret sharing, index coding and locally repairable code. In this paper, by constructing the variable strength arrays of some matroid operations, we characterized matroidal entropy functions induced by regular matroids and some matroids with the same p-characteristic set as uniform matroid $U_{2,4}$.

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arXiv2024

On Decentralized Linearly Separable Computation With the Minimum Computation Cost

The distributed linearly separable computation problem finds extensive applications across domains such as distributed gradient coding, distributed linear transform, real-time rendering, etc. In this paper, we investigate this problem in a fully decentralized scenario, where $\mathsf{N}$ workers collaboratively perform the computation task without a central master. Each worker aims to compute a linearly separable computation that can be manifested as $\mathsf{K}_{\mathrm{c}}$ linear combinations of $\mathsf{K}$ messages, where each message is a function of a distinct dataset. We require that each worker successfully fulfill the task based on the transmissions from any $\mathsf{N}_{\mathrm{r}}$ workers, such that the system can tolerate any $\mathsf{N}-\mathsf{N}_{\mathrm{r}}$ stragglers. We focus on the scenario where the computation cost (the number of uncoded datasets assigned to each worker) is minimum, and aim to minimize the communication cost (the number of symbols the fastest $\mathsf{N}_{\mathrm{r}}$ workers transmit). We propose a novel distributed computing scheme that is optimal under the widely used cyclic data assignment. Interestingly, we demonstrate that the side information at each worker is ineffective in reducing the communication cost when $\mathsf{K}_{\mathrm{c}}\leq {\mathsf{K}}\mathsf{N}_{\mathrm{r}}/{\mathsf{N}}$, while it helps reduce the communication cost as $\mathsf{K}_{\mathrm{c}}$ increases.

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arXiv2023

Asymptotically Optimal Coded Distributed Computing via Combinatorial Designs

Coded distributed computing (CDC) introduced by Li \emph{et al.} can greatly reduce the communication load for MapReduce computing systems. In the general cascaded CDC with $K$ workers, $N$ input files and $Q$ Reduce functions, each input file will be mapped by $r$ workers and each Reduce function will be computed by $s$ workers such that coding techniques can be applied to achieve the maximum multicast gain. The main drawback of most existing CDC schemes is that they require the original data to be split into a large number of input files that grows exponentially with $K$, which can significantly increase the coding complexity and degrade system performance. In this paper, we first use a classic combinatorial structure $t$-design, for any integer $t\geq 2$, to develop a low-complexity and asymptotically optimal CDC with $r=s$. The main advantages of our scheme via $t$-design are two-fold: 1) having much smaller $N$ and $Q$ than the existing schemes under the same parameters $K$, $r$ and $s$; and 2) achieving smaller communication loads compared with the state-of-the-art schemes. Remarkably, unlike the previous schemes that realize on large operation fields, our scheme operates on the minimum binary field $\mathbb{F}_2$. Furthermore, we show that our construction method can incorporate the other combinatorial structures that have a similar property to $t$-design. For instance, we use $t$-GDD to obtain another asymptotically optimal CDC scheme over $\mathbb{F}_2$ that has different parameters from $t$-design. Finally, we show that our construction method can also be used to construct CDC schemes with $r\neq s$ that have small file number and Reduce function number.

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arXiv2023

Coded Caching Schemes for Multiaccess Topologies via Combinatorial Design

This paper studies a multiaccess coded caching (MACC) where the connectivity topology between the users and the caches can be described by a class of combinatorial designs. Our model includes as special cases several MACC topologies considered in previous works. The considered MACC network includes a server containing $N$ files, $Γ$ cache nodes and $K$ cacheless users, where each user can access $L$ cache nodes. The server is connected to the users via an error-free shared link, while the users can retrieve the cache content of the connected cache-nodes while the users can directly access the content in their connected cache-nodes. Our goal is to minimise the worst-case transmission load on the shared link in the delivery phase. The main limitation of the existing MACC works is that only some specific access topologies are considered, and thus the number of users $K$ should be either linear or exponential to $Γ$. We overcome this limitation by formulating a new access topology derived from two classical combinatorial structures, referred to as the $t$-design and the $t$-group divisible design. In these topologies, $K$ scales linearly, polynomially, or even exponentially with $Γ$. By leveraging the properties of the considered combinatorial structures, we propose two classes of coded caching schemes for a flexible number of users, where the number of users can scale linearly, polynomially or exponentially with the number of cache nodes. In addition, our schemes can unify most schemes for the shared link network and unify many schemes for the multi-access network except for the cyclic wrap-around topology.

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arXiv2023

Coded Caching Scheme for Partially Connected Linear Networks Via Multi-antenna Placement Delivery Array

In this paper, we study the coded caching scheme for the $(K,L,M_{\text{T}},M_{\text{U}},N)$ partially connected linear network, where there are $N$ files each of which has an equal size, $K+L-1$ transmitters and $K$ users; each user and transmitter caches at most $M_{\text{U}}$ and $M_{\text{T}}$ files respectively; each user cyclically communicates with $L$ transmitters. The goal is to design caching and delivery schemes to reduce the transmission latency measured by the metric normalized delivery time (NDT). By delicately designing the data placement of the transmitters and users according to the topology, we show that a combinatorial structure called multiple-antenna placement delivery array (MAPDA), which was originally proposed for the multiple-input single-output broadcast channels, can be also used to design schemes for the partially connected linear network. Then, based on existing MAPDAs and our constructing approach, we propose new schemes that achieve the optimal NDT when $ {M_\text{T}}+ {M_\text{U}}\geq N$ and smaller NDT than that of the existing schemes when (${M_\text{T}}+ {M_\text{U}}\leq N$, $\frac{M_\text{U}}{N}+\frac{M_\text{T}}{N} \frac{L}{K}\left\lceil \frac{K}{L} \right\rceil \geq 1$) or ($ {M_\text{U}}+ {M_\text{T}}< N, \frac{K}{L}\notin\mathbb{Z}^+$). Moreover, our schemes operate in one-shot linear delivery and significantly reduce the subpacketizations compared to the existing scheme, which implies that our schemes have a wider range of applications and lower complexity of implementation.

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arXiv2022

Coded Caching Schemes for Two-dimensional Caching-aided Ultra-Dense Networks

Coded caching technique is an efficient approach to reduce the transmission load in networks and has been studied in heterogeneous network settings in recent years. In this paper, we consider a new widespread caching system called $(K_1,K_2,U,r,M,N)$ two-dimensional (2D) caching-aided ultra-dense network (UDN) with a server containing $N$ files, $K_1K_2$ cache nodes arranged neatly on a grid with $K_1$ rows and $K_2$ columns, and $U$ cache-less users randomly distributed around cache nodes. Each cache node can cache at most $M\leq N$ files and has a certain service region by Euclidean distance. The server connects to users through an error-free shared link and the users in the service region of a cache node can freely retrieve all cached contents of this cache node. We aim to design a coded caching scheme for 2D caching-aided UDN systems to reduce the transmission load in the worst case while meeting all possible users' demands. First, we divide all possible users into four classes according to their geographical locations. Then our first order optimal scheme is proposed based on the Maddah-Ali and Niesen scheme. Furthermore, by compressing the transmitted signals of our first scheme based on Maximum Distance Separable (MDS) code, we obtain an improved order optimal scheme with a smaller transmission load.

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arXiv2022

Coded Distributed Computing for Hierarchical Multi-task Learning

In this paper, we consider a hierarchical distributed multi-task learning (MTL) system where distributed users wish to jointly learn different models orchestrated by a central server with the help of a layer of multiple relays. Since the users need to download different learning models in the downlink transmission, the distributed MTL suffers more severely from the communication bottleneck compared to the single-task learning system. To address this issue, we propose a coded hierarchical MTL scheme that exploits the connection topology and introduces coding techniques to reduce communication loads. It is shown that the proposed scheme can significantly reduce the communication loads both in the uplink and downlink transmissions between relays and the server. Moreover, we provide information-theoretic lower bounds on the optimal uplink and downlink communication loads, and prove that the gaps between achievable upper bounds and lower bounds are within the minimum number of connected users among all relays. In particular, when the network connection topology can be delicately designed, the proposed scheme can achieve the information-theoretic optimal communication loads. Experiments on real datasets show that our proposed scheme can reduce the overall training time by 17% $\sim$ 26% compared to the conventional uncoded scheme.

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arXiv2022

Centralized Hierarchical Coded Caching Scheme over Two-Layer Networks

This paper considers a hierarchical caching system where a server connects with multiple mirror sites, each connecting with a distinct set of users, and both the mirror sites and users are equipped with caching memories. Although there already exist works studying this setup and proposing coded caching scheme to reduce transmission loads, two main problems are remained to address: 1) the optimal communication load under the uncoded placement for the first hop, denoted by $R_1$, is still unknown. 2) the previous schemes are based on Maddah-Ali and Niesen's data placement and delivery, which requires high subpacketization level. How to achieve the well tradeoff between transmission loads and subpacketization level for the hierarchical caching system is unclear. In this paper, we aim to address these two problems. We first propose a new combination structure named hierarchical placement delivery array (HPDA), which characterizes the data placement and delivery for any hierarchical caching system. Then we construct two classes of HPDAs, where the first class leads to a scheme achieving the optimal $R_1$ for some cases, and the second class requires a smaller subpacketization level at the cost of slightly increasing transmission loads.

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arXiv2022

Hierarchical Cache-Aided Linear Function Retrieval with Security and Privacy Constraints

The hierarchical caching system where a server connects with multiple mirror sites, each connecting with a distinct set of users, and both the mirror sites and users are equipped with caching memories has been widely studied. However all the existing works focus on single file retrieval, i.e., each user requests one file, and ignore the security and privacy threats in communications. In this paper we investigate the linear function retrieval problem for hierarchical caching systems with content security and demand privacy, i.e., each user requests a linear combination of files, and meanwhile the files in the library are protected against wiretappers and users' demands are kept unknown to other users and unconnected mirror sites. First we propose a new combination structure named hierarchical placement delivery array (HPDA), which characterizes the data placement and delivery strategy of a coded caching scheme. Then we construct two classes of HPDAs. Consequently two classes of schemes with or without security and privacy are obtained respectively where the first dedicates to minimizing the transmission load for the first hop and can achieve the optimal transmission load for the first hop if ignoring the security and privacy constraints; the second has more flexible parameters on the memory sizes and a lower subpacketization compared with the first one, and achieves a tradeoff between subpacketization and transmission loads.

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arXiv2022

Multi-access Coded Caching with Optimal Rate and Linear Subpacketization under PDA and Consecutive Cyclic Placement

This work considers the multi-access caching system proposed by Hachem et al., where each user has access to L neighboring caches in a cyclic wrap-around fashion. We first propose a placement strategy called the consecutive cyclic placement, which achieves the maximal local caching gain. Then under the consecutive cyclic placement, we derive the optimal coded caching gain from the perspective of Placement Delivery Array (PDA), thus obtaining a lower bound on the rate of PDA. Finally, under the consecutive cyclic placement, we construct a class of PDA, leading to a multi-access coded caching scheme with linear subpacketization, which achieves our derived lower bound for some parameters; while for other parameters, the achieved coded caching gain is only 1 less than the optimal one. Analytical and numerical comparisons of the proposed scheme with existing schemes are provided to validate the performance.

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arXiv2022

Design of Coded Caching Schemes with Linear Subpacketizations Based on Injective Arc Coloring of Regular Digraphs

Coded caching is an effective technique to decongest the amount of traffic in the backhaul link. In such a scheme, each file hosted in the server is divided into a number of packets to pursue a low transmission rate based on the delicate design of contents cached into users and broadcast messages. However, the implementation complexity of this scheme increases with the number of packets. It is desirable to design a scheme with a small subpacketization level and a relatively low transmission rate. Recently, placement delivery array (PDA) was proposed to address the subpacketization bottleneck of coded caching. This paper investigates the design PDA from a new perspective, i.e., the injective arc coloring of regular digraphs. It is shown that the injective arc coloring of a regular digraph can yield a PDA with the same number of rows and columns. Based on this, a new class of regular digraphs are defined and the upper bounds on the injective chromatic index of such digraphs are derived. Consequently, some new coded caching schemes with a linear subpacketization level and a small transmission rate are proposed, one of which generalizes the existing scheme for the scenario with a more flexible number of users.

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arXiv2022

Coded Caching for Two-Dimensional Multi-Access Networks

This paper studies a novel multi-access coded caching (MACC) model in the two-dimensional (2D) topology, which is a generalization of the one-dimensional (1D) MACC model proposed by Hachem et al. The 2D MACC model is formed by a server containing $N$ files, $K_1\times K_2$ cache-nodes with $M$ files located at a grid with $K_1$ rows and $K_2$ columns, and $K_1\times K_2$ cache-less users where each user is connected to $L^2$ nearby cache-nodes. The server is connected to the users through an error-free shared link, while the users can retrieve the cached content of the connected cache-nodes without cost. Our objective is to minimize the worst-case transmission load over all possible users' demands. In this paper, we first propose a grouping scheme for the case where $K_1$ and $K_2$ are divisible by $L$. By partitioning the cache-nodes and users into $L^2$ groups such that no two users in the same group share any cache-node, we use the shared-link coded caching scheme proposed by Maddah-Ali and Niesen for each group. Then for any model parameters satisfying $\min\{K_1,K_2\}>L$, we propose a transformation approach which constructs a 2D MACC scheme from two classes of 1D MACC schemes in vertical and horizontal projections, respectively. As a result, we can construct 2D MACC schemes that achieve maximum local caching gain and improved coded caching gain, compared to the baseline scheme by a direct extension from 1D MACC schemes.

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arXiv2022

On the Optimal Memory-Load Tradeoff of Coded Caching for Location-Based Content

Caching at the wireless edge nodes is a promising way to boost the spatial and spectral efficiency, for the sake of alleviating networks from content-related traffic. Coded caching originally introduced by Maddah-Ali and Niesen significantly speeds up communication efficiency by transmitting multicast messages simultaneously useful to multiple users. Most prior works on coded caching are based on the assumption that each user may request all content in the library. However, in many applications the users are interested only in a limited set of content that depends on their location. Motivated by these considerations, this paper formulates the coded caching problem for location-based content with edge cache nodes. The considered problem includes a content server with access to $N$ location-based files (e.g., High-Definition maps), $K$ edge cache nodes located at different regions, and $K$ users (i.e., vehicles) each of which is in the serving region of one cache node and can retrieve the cached content of this cache node with negligible cost. Depending on the location, each user only requests a file from a location-dependent subset of the library. The objective is to minimize the worst-case load. For this novel coded caching problem, we propose a highly non-trivial converse bound under uncoded cache placement, which shows that a simple achievable scheme is optimal under uncoded cache placement. In addition, this achievable scheme is also proved to be generally order optimal within a factor of $3$. Finally, we extend the coded caching problem for location-based content to the multiaccess coded caching topology originally proposed by Hachem et al., where each user is connected to $L$ nearest cache nodes. When $L \geq 2$, we characterize the exact optimality on the worst-case load.

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arXiv2022

Multiple-antenna Placement Delivery Array for Cache-aided MISO Systems

We consider the cache-aided multiple-input single-output (MISO) broadcast channel, which consists of a server with $L$ antennas and $K$ single-antenna users, where the server contains $N$ files of equal length and each user is equipped with a local cache of size $M$ files. Each user requests an arbitrary file from library. The objective is to design a coded caching scheme based on uncoded placement and one-shot linear delivery, to achieve the maximum sum Degree-of-Freedom (sum-DoF) with low subpacketization. It was shown in the literature that under the constraint of uncoded placement and one-shot linear delivery, the optimal sum-DoF is $L+\frac{KM}{N}$. However, previously proposed schemes for this setting incurred either an exponential subpacketization order in $K$, or required specific conditions in the system parameters $L$, $K$, $M$ and $N$. In this paper, we propose a new combinatorial structure called multiple-antenna placement delivery array (MAPDA). Based on MAPDA and Latin square, the first proposed scheme achieves the optimal sum-DoF $L+\frac{KM}{N}$ with the subpacketization of $K$ when $\frac{KM}{N}+L=K$. Subsequently, for the general case we propose a transformation approach to construct an MAPDA from any $g$-regular PDA (a class of PDA where each integer in the array occurs $g$ times) for the original shared-link coded caching problem. When the original PDA corresponds to the Maddah-Ali and Niesen coded caching scheme, the resulting scheme under the combinatorial structure of MAPDA can achieve the optimal sum-DoF $L+\frac{KM}{N}$ with reduced subpacketization with respect to the existing schemes. The work can be extended to the multiple independent single-antenna transmitters (servers) corresponding to the cache-aided interference channel proposed by Naderializadeh et al. and the scenario of transmitters equipped with multiple antennas.

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