Coding theoretic approached have been developed to significantly reduce the communication load in modern distributed computing system. In particular, coded distributed computing (CDC) introduced by Li et al. can efficiently trade computation resources to reduce the communication load in MapReduce like computing systems. For the more general cascaded CDC, Map computations are repeated at r nodes to significantly reduce the communication load among nodes tasked with computing Q Reduce functions s times. In this paper, we propose a novel low-complexity combinatorial design for cascaded CDC which 1) determines both input file and output function assignments, 2) requires significantly less number of input files and output functions, and 3) operates on heterogeneous networks where nodes have varying storage and computing capabilities. We provide an analytical characterization of the computation-communication tradeoff, from which we show the proposed scheme can outperform the state-of-the-art scheme proposed by Li et al. for the homogeneous networks. Further, when the network is heterogeneous, we show that the performance of the proposed scheme can be better than its homogeneous counterpart. In addition, the proposed scheme is optimal within a constant factor of the information theoretic converse bound while fixing the input file and the output function assignments.
Li {\it et al}. introduced coded distributed computing (CDC) scheme to reduce the communication load in general distributed computing frameworks such as MapReduce. They also proposed cascaded CDC schemes where each output function is computed multiple times, and proved that such schemes achieved the fundamental trade-off between computation load and communication load. However, these schemes require exponentially large numbers of input files and output functions when the number of computing nodes gets large. In this paper, by using the structure of placement delivery arrays (PDAs), we construc…
Coded distributed computing (CDC) introduced by Li et al. in 2015 offers an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce. For the more general cascaded CDC, Map computations are repeated at $r$ nodes to significantly reduce the communication load among nodes tasked with computing $Q$ Reduce functions $s$ times. While an achievable cascaded CDC scheme was proposed, it only operates on homogeneous networks, where the storage, computation load and communication load of each computing node is the same. In…
Coded distributed computing introduced by Li et al. in 2015 is an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce. In particular, Li et al. show that increasing the computation load in the Map phase by a factor of $r$ can create coded multicasting opportunities to reduce the communication load in the Reduce phase by the same factor. However, there are two major limitations in practice. First, it requires an exponentially large number of input files (data batches) when the number of computing nodes gets l…
Coded Distributed Computing (CDC) introduced by Li et al. in 2015 offers an efficient approach to trade computing power to reduce the communication load in general distributed computing frameworks such as MapReduce and Spark. In particular, increasing the computation load in the Map phase by a factor of r can create coded multicasting opportunities to reduce the communication load in the Shuffle phase by the same factor. However, the CDC scheme is designed for the homogeneous settings, where the storage, computation load and communication load on the computing nodes are the same. In addition, …
Coded caching is an efficient way to reduce network traffic congestion during peak hours by storing some content at the user's local cache memory without knowledge of later demands. The goal of coded caching design is to minimize the transmission rate and the subpacketization. In practice the demand for each user is sensitive since one can get the other users' preferences when it gets the other users' demands. The first coded caching scheme with private demands was proposed by Wan et al. However the transmission rate and the subpacketization of their scheme increase with the file number stored…
Recently, Muralidhar et al. proposed a novel multi-access system model where each user is connected to multiple caches in a manner that follows the well-known combinatorial topology of combination networks. For such multi-access topology, the same authors proposed an achievable scheme, which stands out for the unprecedented coding gains even with very modest cache resources. In this paper, we identify the fundamental limits of such multi-access setting with exceptional potential, providing an information-theoretic converse which establishes, together with the inner bound by Muralidhar et al., …
We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called \textit{cache}) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. In this work, we propose a binary matrix model to cons…
We consider the standard broadcast setup with a single server broadcasting information to a number of clients, each of which contains local storage (called cache) of some size, which can store some parts of the available files at the server. The centralized coded caching framework, consists of a caching phase and a delivery phase, both of which are carefully designed in order to use the cache and the channel together optimally. In prior literature, various combinatorial structures have been used to construct coded caching schemes. One of the chief drawbacks of many of these existing constructi…
Consider a multi-cell mobile edge computing network, in which each user wishes to compute the product of a user-generated data matrix with a network-stored matrix. This is done through task offloading by means of input uploading, distributed computing at edge nodes (ENs), and output downloading. Task offloading may suffer long delay since servers at some ENs may be straggling due to random computation time, and wireless channels may experience severe fading and interference. This paper aims to investigate the interplay among upload, computation, and download latencies during the offloading pro…
We study the problem of constructing centralized coded caching schemes with low subpacketization level based on the placement delivery array (PDA) design framework. PDA design is an efficient way to construct centralized coded caching schemes and most existing schemes, including the famous Maddah-Ali-Niesen scheme, can be described using PDA. In this paper, we first prove that constructing a PDA is equivalent to constructing three binary matrices that satisfy certain conditions. From this perspective, we then propose some new constructions of coded caching schemes using PDA design based on pro…
Coded caching is a technique that generalizes conventional caching and promises significant reductions in traffic over caching networks. However, the basic coded caching scheme requires that each file hosted in the server be partitioned into a large number (i.e., the subpacketization level) of non-overlapping subfiles. From a practical perspective, this is problematic as it means that prior schemes are only applicable when the size of the files is extremely large. In this work, we propose coded caching schemes based on combinatorial structures called resolvable designs. These structures can be…
Coded caching systems have been widely studied to reduce the data transmission during the peak traffic time. In practice, two important parameters of a coded caching system should be considered, i.e., the rate which is the maximum amount of the data transmission during the peak traffic time, and the subpacketization level, the number of divided packets of each file when we implement a coded caching scheme. We prefer to design a scheme with rate and packet number as small as possible since they reflect the transmission efficiency and complexity of the caching scheme, respectively. In this paper…
The pragmatic approach to coded continuous-phase modulation (CPM) is proposed as a capacity-achieving low-complexity alternative to the serially-concatenated CPM (SC-CPM) coding scheme. In this paper, we first perform a selection of the best spectrally-efficient CPM modulations to be embedded into SC-CPM schemes. Then, we consider the pragmatic capacity (a.k.a. BICM capacity) of CPM modulations and optimize it through a careful design of the mapping between input bits and CPM waveforms. The so obtained schemes are cascaded with an outer serially-concatenated convolutional code to form a pragma…
Several network communication problems are highly related such as coded caching and distributed computation. The centralized coded caching focuses on reducing the network burden in peak times in a wireless network system and the coded distributed computation studies the tradeoff between computation and communication in distributed system. In this paper, motivated by the study of the only rainbow $3$-term arithmetic progressions set, we propose a unified framework for constructing coded caching schemes. This framework builds bridges between coded caching schemes and lots of combinatorial object…
We consider a centralized caching network, where a server serves several groups of users, each having a common shared homogeneous fixed-size cache and requesting arbitrary multiple files. An existing coded prefetching scheme is employed where each file is broken into multiple fragments and each cache stores multiple coded packets each formed by XORing fragments from different files. For such a system, we propose an efficient file delivery scheme with explicit constructions by the server to meet the arbitrary multi-requests of all user-groups. Specifically, the stored coded packets of each cach…
Coded caching can significantly reduce the communication bandwidth requirement for satisfying users' demands by utilizing the multicasting gain among multiple users. Most existing works assume that the users follow the prescriptions for content placement made by the system. However, users may prefer to decide what files to cache. To address this issue, we consider a network consisting of a file server connected through a shared link to $K$ users, each equipped with a cache which has been already filled arbitrarily. Given an arbitrary content placement, the goal is to find a delivery strategy f…
In an $(H,r)$ combination network, a single content library is delivered to ${H\choose r}$ users through deployed $H$ relays without cache memories, such that each user with local cache memories is simultaneously served by a different subset of $r$ relays on orthogonal non-interfering and error-free channels. The combinatorial placement delivery array (CPDA in short) can be used to realize a coded caching scheme for combination networks. In this paper, a new algorithm realizing a coded caching scheme for combination network based on a CPDA is proposed such that the schemes obtained have smalle…
A multi-access network consisting of $N$ files, $C$ caches, $K$ users with each user having access to a unique set of $r$ caches has been introduced recently by Muralidhar et al. ("Maddah-Ali-Niesen Scheme for Multi-access Coded Caching," in \textit{Proc. ITW}, 2021). It considers Single File Retrieval (SFR) i.e, each user demands an arbitrary file from the server. It proposes a coded caching scheme which was shown to be optimal under the assumption of uncoded placement by Brunero and Elia ("Fundamental Limits of Combinatorial Multi-Access Caching" in {\textit{arXiv:2110.07426} }). The above m…
Coded caching scheme, which is an effective technique to increase the transmission efficiency during peak traffic times, has recently become quite popular among the coding community. Generally rate can be measured to the transmission in the peak traffic times, i.e., this efficiency increases with the decreasing of rate. In order to implement a coded caching scheme, each file in the library must be split in a certain number of packets. And this number directly reflects the complexity of a coded caching scheme, i.e., the complexity increases with the increasing of the packet number. However ther…
We study the optimal design of heterogeneous Coded Elastic Computing (CEC) where machines have varying computation speeds and storage. CEC introduced by Yang et al. in 2018 is a framework that mitigates the impact of elastic events, where machines can join and leave at arbitrary times. In CEC, data is distributed among machines using a Maximum Distance Separable (MDS) code such that subsets of machines can perform the desired computations. However, state-of-the-art CEC designs only operate on homogeneous networks where machines have the same speeds and storage. This may not be practical. In th…
In a traditional $(H, r)$ combination network, each user is connected to a unique set of $r$ relays. However, few research efforts to consider $(H, r, u)$ multiaccess combination network problem where each $u$ users are connected to a unique set of $r$ relays. A naive strategy to obtain a coded caching scheme for $(H, r, u)$ multiaccess combination network is by $u$ times repeated application of a coded caching scheme for a traditional $(H, r)$ combination network. Obviously, the transmission load for each relay of this trivial scheme is exactly $u$ times that of the original scheme, which imp…
Caching prefetches some library content at users' memories during the off-peak times (i.e., {\it placement phase}), such that the number of transmissions during the peak-traffic times (i.e., {\it delivery phase}) are reduced. A coded caching strategy was originally proposed by Maddah-Ali and Niesen (MN) leading to a multicasting gain compared to the conventional uncoded caching, where each message in the delivery phase is useful to multiple users simultaneously. However, the MN coded caching scheme suffers from the high subpacketization which makes it impractical. In order to reduce the subpac…
We consider wireless device-to-device (D2D) caching networks with single-hop transmissions. Previous work has demonstrated that caching and coded multicasting can significantly increase per user throughput. However, the state-of-the-art coded caching schemes for D2D networks are generally impractical because content files are partitioned into an exponential number of packets with respect to the number of users if both library and memory sizes are fixed. In this paper, we present two combinatorial approaches of D2D coded caching network design with reduced packetizations and desired throughput …
We study the problem of multi-access coded caching (MACC): a central server has $N$ files, $K$ ($K \leq N$) caches each of which stores $M$ out of the $N$ files, $K$ users each of which demands one out of the $N$ files, and each user accesses $z$ caches. The objective is to jointly design the placement, delivery, and user-to-cache association, to optimize the achievable rate. This problem has been extensively studied in the literature under the assumption that a user accesses only one cache. However, when a user accesses more caches, this problem has been studied only under the assumption that…
We consider the "coded cooperative data exchange problem" for general graphs. In this problem, given a graph G=(V,E) representing clients in a broadcast network, each of which initially hold a (not necessarily disjoint) set of information packets; one wishes to design a communication scheme in which eventually all clients will hold all the packets of the network. Communication is performed in rounds, where in each round a single client broadcasts a single (possibly encoded) information packet to its neighbors in G. The objective is to design a broadcast scheme that satisfies all clients with t…
Coded distributed computing (CDC) is a new technique proposed with the purpose of decreasing the intense data exchange required for parallelizing distributed computing systems. Under the famous MapReduce paradigm, this coded approach has been shown to decrease this communication overhead by a factor that is linearly proportional to the overall computation load during the mapping phase. Nevertheless, it is widely accepted that this overhead remains a main bottleneck in distributed computing. To address this, we take a new approach and we explore a new system model which, for the same aforementi…
We consider a cache-aided interference network which consists of a library of $N$ files, $K_T$ transmitters and $K_R$ receivers (users), each equipped with a local cache of size $M_T$ and $M_R$ files respectively, and connected via a discrete-time additive white Gaussian noise (AWGN) channel. Each receiver requests an arbitrary file from the library. The objective is to design a cache placement without knowing the receivers' requests and a communication scheme such that the sum Degrees of Freedom (sum-DoF) of the delivery is maximized. This network model with one-shot transmission was firstly …
We consider the distributed computing framework of MapReduce, which consists of three phases, the Map phase, the Shuffle phase and the Reduce phase. For this framework, we propose the use of binary matrices (with $0,1$ entries) called \textit{computing matrices} to describe the map phase and the shuffle phase. Similar binary matrices were recently proposed for the coded caching framework. The structure of ones and zeroes in the binary computing matrix captures the map phase of the MapReduce framework. We present a new simple coded data shuffling scheme for this binary matrix model, based on a …
Large scale clusters leveraging distributed computing frameworks such as MapReduce routinely process data that are on the orders of petabytes or more. The sheer size of the data precludes the processing of the data on a single computer. The philosophy in these methods is to partition the overall job into smaller tasks that are executed on different servers; this is called the map phase. This is followed by a data shuffling phase where appropriate data is exchanged between the servers. The final so-called reduce phase, completes the computation. One potential approach, explored in prior work fo…
Distributed computing frameworks such as MapReduce are often used to process large computational jobs. They operate by partitioning each job into smaller tasks executed on different servers. The servers also need to exchange intermediate values to complete the computation. Experimental evidence suggests that this so-called Shuffle phase can be a significant part of the overall execution time for several classes of jobs. Prior work has demonstrated a natural tradeoff between computation and communication whereby running redundant copies of jobs can reduce the Shuffle traffic load, thereby leadi…
