arXiv subjects

B. Sundar Rajan

Publications and source records attributed to B. Sundar Rajan.

At least 55 records · Page 3Linked to original sources

arXiv2024

Coded Caching with Shared Caches and Private Caches

This work studies the coded caching problem in a setting where the users are simultaneously endowed with a private cache and a shared cache. The setting consists of a server connected to a set of users, assisted by a smaller number of helper nodes that are equipped with their own storage. In addition to the helper cache, each user possesses a dedicated cache which is also used to prefetch file contents. Each helper cache can serve an arbitrary number of users, but each user gets served by only one helper cache. We consider two scenarios: (a) the server has no prior information about the user-to-helper cache association, and (b) the server knows the user-to-helper cache association at the placement phase itself. We design centralized coded caching schemes under uncoded placement for the above two settings. For case (b), two schemes are proposed that are optimal in certain memory regimes. Further, a cut-set based lower bound is derived and used to show that one of the proposed schemes for case (b) is optimal in certain memory regime.

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arXiv2024

Optimal Placement Delivery Arrays from $t$-Designs with Application to Hierarchical Coded Caching

Coded caching scheme originally proposed by Maddah-Ali and Niesen (MN) achieves an optimal transmission rate $R$ under uncoded placement but requires a subpacketization level $F$ which increases exponentially with the number of users $K$ where the number of files $N \geq K$. Placement delivery array (PDA) was proposed as a tool to design coded caching schemes with reduced subpacketization level by Yan \textit{et al.} in \cite{YCT}. This paper proposes two novel classes of PDA constructions from combinatorial $t$-designs that achieve an improved transmission rate for a given low subpacketization level, cache size and number of users compared to existing coded caching schemes from $t$-designs. A $(K, F, Z, S)$ PDA composed of a specific symbol $\star$ and $S$ non-negative integers corresponds to a coded caching scheme with subpacketization level $F$, $K$ users each caching $Z$ packets and the demands of all the users are met with a rate $R=\frac{S}{F}$. For a given $K$, $F$ and $Z$, a lower bound on $S$ such that a $(K, F, Z, S)$ PDA exists is given by Cheng \textit{et al.} in \cite{MJXQ} and by Wei in \cite{Wei} . Our first class of proposed PDA achieves the lower bound on $S$. The second class of PDA also achieves the lower bound in some cases. From these two classes of PDAs, we then construct hierarchical placement delivery arrays (HPDA), proposed by Kong \textit{et al.} in \cite{KYWM}, which characterizes a hierarchical two-layer coded caching system. These constructions give low subpacketization level schemes.

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arXiv2024

Multi-access Distributed Computing Models from Map-Reduce Arrays

A novel distributed computing model called "Multi-access Distributed Computing (MADC)" was recently introduced in http://www.arXiv:2206.12851. In this paper, we represent MADC models via 2-layered bipartite graphs called Map-Reduce Graphs (MRGs) and a set of arrays called Map-Reduce Arrays (MRAs) inspired from the Placement Delivery Arrays (PDAs) used in the coded caching literature. The connection between MRAs and MRGs is established, thereby exploring new topologies and providing coded shuffling schemes for the MADC models with MRGs using the structure of MRAs. A novel \textit{Nearest Neighbor Connect-MRG (NNC-MRG)} is explored and a coding scheme is provided for MADC models with NNC-MRG, exploiting the connections between MRAs and PDAs. Moreover, CT is generalized to Generalized Combinatorial-MRG (GC-MRG). A set of $g-$regular MRAs is provided which corresponds to the existing scheme for MADC models with CT and extended those to generate another set of MRAs to represent MADC models with GC-MRG. A lower bound on the computation-communication curve for MADC model with GC-MRG under homogeneous setting is derived and certain cases are explored where the existing scheme is optimal under CT. One of the major limitations of the existing scheme for CT is that it requires an exponentially large number of reducer nodes and input files for large $Λ$. This can be overcome by representing CT by MRAs, where coding schemes can be derived even if some of the reducer nodes are not present. Another way of tackling this is by using a different MRG, specifically NNC-MRG, where the number of reducer nodes and files required are significantly smaller compared to CT. Hence, the advantages are two-fold, which is achievable at the expense of a slight increase in the communication load.

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arXiv2024

Improved Hotplug Caching Schemes Using PDAs and t-Designs

We consider a coded caching system in which some users are offline at the time of delivery. Such systems are called hotplug coded caching systems. A placement delivery array (PDA) is a well-known tool for constructing a coded caching scheme for dedicated caches. In this paper, we introduce the concept of PDAs for hotplug coded caching schemes and refer to it as a hotplug placement delivery array (HpPDA). We give an algorithm to describe the placement and the delivery phase of a hotplug coded caching scheme using HpPDA. We show that an existing hotplug coded caching scheme given by Y. Ma and D. Tuninetti in 2022 corresponds to a class of HpPDAs and then propose a method to further improve the rate of that scheme. Additionally, we construct a class of HpPDAs using $t$-designs, which corresponds to a scheme for hotplug coded caching systems. We further improve the rate of this scheme and prove that the cut-set bound is achieved in some higher memory range for a hotplug coded caching system with three active users.

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arXiv2024

Combinatorial Multi-Access Coded Caching: Improved Rate-Memory Trade-off with Coded Placement

This work considers the combinatorial multi-access coded caching problem introduced in the recent work by Muralidhar \textit{et al.} [P. N. Muralidhar, D. Katyal, and B. S. Rajan, ``Maddah-Ali-Niesen scheme for multi-access coded caching,'' in \textit{IEEE Inf. Theory Workshop (ITW)}, 2021] The problem setting consists of a central server having a library of $N$ files and $C$ caches each with capacity $M$. Each user in the system can access a unique set of $r N/C$. For a lower memory regime, we present another scheme with coded placement, which outperforms the optimal scheme under uncoded placement if the number of files is no more than the number of users. Further, we derive an information-theoretic lower bound on the optimal rate-memory trade-off of the combinatorial multi-access coded caching scheme. In addition, using the derived lower bound, we show that the first scheme is optimal in the higher memory regime, and the second scheme is optimal if $N\leq \binom{C}{r}$. Finally, we show that the performance of the first scheme is within a constant factor of the optimal performance, when $r=2$.

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arXiv2023

An Optimal Two-Step Decoding at Receivers with Side Information in PSK-Modulated Index Coding

This paper studies noisy index coding problems over single-input single-output broadcast channels. The codewords from a chosen index code of length $N$ are transmitted after $2^N$-PSK modulation over an AWGN channel. In "Index Coded PSK Modulation for prioritized Receivers," the authors showed that when a length-$N$ index code is transmitted as a $2^N$-PSK symbol, the ML decoder at a receiver decodes directly to the message bit rather than following the two-step decoding process of first demodulating the PSK symbol and equivalently the index-coded bits and then doing index-decoding. In this paper, we consider unprioritized receivers and follow the two-step decoding process at the receivers. After estimating the PSK symbol using an ML decoder, at a receiver, there might be more than one decoding strategy, i.e., a linear combination of index-coded bits and different subsets of side information bits, that can be used to estimate the requested message. Thomas et al. in ["Single Uniprior Index Coding With Min Max Probability of Error Over Fading Channels,"] showed that for binary-modulated index code transmissions, minimizing the number of transmissions used to decode a requested message is equivalent to minimizing the probability of error. This paper shows that this is no longer the case while employing multi-level modulations. Further, we consider that the side information available to each receiver is also noisy and derive an expression for the probability that a requested message bit is estimated erroneously at a receiver. We also show that the criterion for choosing a decoding strategy that gives the best probability of error performance at a receiver changes with the signal-to-noise ratio at which the side information is broadcast.

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arXiv2023

Design and Analysis of Index codes for 3-Group NOMA in Vehicular Adhoc Networks

Index coding (IC) is a source coding technique employed to improve spectral utilisation, where the source node aims to satisfy users' demands by making minimum transmissions. Non-orthogonal multiple access (NOMA) is integral to the radio access technique used in 5G networks. Index-coded NOMA (IC-NOMA) transmission scheme in Vehicular Adhoc Networks (VANETs) involves applying NOMA principles on index-coded data to avoid network congestion and to improve spectral efficiency compared to conventional IC systems. In this work, a spectral efficient transmission scheme called 3-Group IC-NOMA is proposed, and an innovative index code design that fits with NOMA decoding principles to obtain improved spectral efficiency is developed. Through exhaustive analytical studies, we demonstrate that the proposed transmission scheme always supports higher rates than the conventional IC systems and requires less power to achieve an information rate at least as good as conventional IC systems.

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arXiv2023

On Cache-Aided Multi-User Private Information Retrieval with Small Caches

In this paper, we propose a scheme for the problem of cache-aided multi-user private information retrieval with small caches, in which $K$ users are connected to $S$ non-colluding databases via shared links. Each database contains a set of $N$ files, and each user has a dedicated cache of size equivalent to the size of $M$ files. All the users want to retrieve a file without revealing their demands to the databases. During off-peak hours, all the users will fill their caches, and when required, users will demand their desired files by cooperatively generating query sets for each database. After receiving the transmissions from databases, all the users should get their desired files using transmitted data and their cache contents. This problem has been studied in [X. Zhang, K. Wan, H. Sun, M. Ji and G. Caire, \tqt{Fundamental limits of cache-aided multiuser private information retrieval}, IEEE Trans. Commun., 2021], in which authors proposed a product design scheme. In this paper, we propose a scheme that gives a better rate for a particular value of $M$ than the product design scheme. We consider a slightly different approach for the placement phase. Instead of a database filling the caches of all users directly, a database will broadcast cache content for all users on a shared link, and then the users will decide unitedly which part of the broadcasted content will be stored in the cache of each user. This variation facilitates maintaining the privacy constraint at a reduced rate.

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arXiv2023

Security and Privacy in Cache-Aided Linear Function Retrieval for Multi-access Coded Caching

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 multi-access network is referred to as combinatorial topology which is considered in this work with three additional features : a) Linear Function Retrieval (LFR) i.e., each user is interested in retrieving an arbitrary linear combination of files in the server's library; b) Security i.e., the content of the library must be kept secure from an eavesdropper who obtains the signal sent by the server; c) Privacy i.e., each user can only get its required file and can not get any information about the demands of other users. Achievable Secure, Private LFR (SP-LFR) scheme, Secure LFR (S-LFR) scheme and Improved S-LFR scheme are proposed. As special cases, our work recovers some of the results by Yan and Tuninetti ("Key Superposition Simultaneously Achieves Security and Privacy in Cache-Aided Linear Function Retrieval," in \textit{Trans. Inf. Forensics and Security}, 2021") and Sengupta et al.("Fundamental limits of caching with secure delivery," in \textit{Trans. Inf. Forensics and Security}, 2015). At a memory point, $M=\frac{r\binom{C}{r}}{C}$, the SP-LFR scheme is within a constant multiplicative factor from the optimal rate for $N\geq2Kr$ and at, $M=\frac{\binom{C}{r}}{C}$, the improved S-LFR scheme is within a constant multiplicative factor from the optimal rate for $N\geq2K$.

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arXiv2022

Shared Cache Coded Caching Schemes Using Designs and Circuits of Matrices

In this paper, we study shared cache coded caching (SC-CC): a set of caches serves a larger set of users; each user access one cache, and a cache may serve many users. For this problem, under uncoded placement, Parrinello, Ünsal, and Elia showed an optimal SC-CC scheme, in which the subpacketization level depends upon the number of caches. We show an SC-CC scheme where the subpacketization level does not directly depend upon the number of users or caches; any number of caches and users can be accommodated for a fixed subpacketization level. Furthermore, new caches can be added without re-doing the placement of the existing caches. We show that given an upper limit on the allowable subpacketization level, our SC-CC scheme may achieve a lesser rate than other relevant SC-CC schemes. Our scheme is constructed using matrices and designs. A matroid can be obtained from a matrix over a finite field; the placement of our scheme is decided by a design constructed from a matrix; the circuits of a matroid obtained from the matrix and the design is used to decide the delivery.

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arXiv2022

Multi-Access Coded Caching Schemes from Maximal Cross Resolvable Designs

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 a user accesses $z$ consecutive caches with a cyclic wrap-around over the boundaries. A natural question is how other user-to-cache associations fare against the cyclic wrap-around user-to-cache association. A bipartite graph can describe a general user-to-cache association. We identify a class of bipartite graphs that, when used as a user-to-cache association, achieves either a lesser rate or a lesser subpacketization than all other existing MACC schemes using a cyclic wrap-around user-to-cache association. The placement and delivery strategy of our MACC scheme is constructed using a combinatorial structure called maximal cross resolvable design.

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arXiv2022

Shared Cache Coded Caching Schemes with known User-to-Cache Association Profile using Placement Delivery Arrays

This work considers the coded caching problem with shared caches, where users share the caches, and each user gets access only to one cache. The user-to-cache association is assumed to be known at the server during the placement phase. We focus on the schemes derived using placement delivery arrays (PDAs). The PDAs were originally designed to address the sub-packetization bottleneck of coded caching in a dedicated cache setup. We observe that in the setup of this paper permuting the columns of the PDA results in schemes with different performance for the same problem, but the sub-packetization level remains the same. This is contrary to what was observed for dedicated cache networks. We propose a procedure to identify the ordering of columns that gives the best performance possible for the PDA employed for the given problem. Further, some specific classes of PDAs are chosen and the performance gain achieved by reordering the columns of the PDA is illustrated.

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arXiv2022

Extended Placement Delivery Arrays for Multi-Antenna Coded Caching Scheme

The multi-antenna coded caching problem, where the server having $L$ transmit antennas communicating to $K$ users through a wireless broadcast link, is addressed. In the problem setting, the server has a library of $N$ files, and each user is equipped with a dedicated cache of capacity $M$. The idea of extended placement delivery array (EPDA), an array which consists of a special symbol $\star$ and integers in a set $\{1,2,\dots,S\}$, is proposed to obtain a novel solution for the aforementioned multi-antenna coded caching problem. From a $(K,L,F,Z,S)$ EPDA, a multi-antenna coded caching scheme with $K$ users, and the server with $L$ transmit antennas, can be obtained in which the normalized memory $\frac{M}{N}=\frac{Z}{F}$, and the delivery time $T=\frac{S}{F}$. The placement delivery array (for single-antenna coded caching scheme) is a special class of EPDAs with $L=1$. For the multi-antenna coded caching schemes constructed from EPDAs, it is shown that the maximum possible Degree of Freedom (DoF) that can be achieved is $t+L$, where $t=\frac{KM}{N}$ is an integer. Furthermore, two constructions of EPDAs are proposed: a) $ K=t+L$, and b) $K=nt+(n-1)L, \hspace{0.1cm}L\geq t$, where $n\geq 2$ is an integer. In the resulting multi-antenna schemes from those EPDAs achieve the full DoF, while requiring a subpacketization number $\frac{K}{\text{gcd}(K,t,L)}$. This subpacketization number is less than that required by previously known schemes in the literature.

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arXiv2022

An Improved Lower Bound for Multi-Access Coded Caching

The multi-access variant of the coded caching problem with $N$ files, $K$ users and $K$ caches, where each user has access to $L$ neighbouring caches in a cyclic wrap-around manner, is considered. A cut-set based lower bound on the optimal rate-memory trade-off of the multi-access coded caching (MACC) scheme is derived. Furthermore, an improved lower bound on the optimal rate-memory trade-off of the MACC scheme is derived using non-cut-set arguments. The improved lower bound is tighter than the previously known lower bounds for the same setting.

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arXiv2022

Minrank of Embedded Index Coding Problems and its Relation to Connectedness of a Bipartite Graph

This paper deals with embedded index coding problem (EICP), introduced by A. Porter and M. Wootters, which is a decentralized communication problem among users with side information. An alternate definition of the parameter minrank of an EICP, which has reduced computational complexity compared to the existing definition, is presented. A graphical representation for an EICP is given using directed bipartite graphs, called bipartite problem graph, and the side information alone is represented using an undirected bipartite graph called the side information bipartite graph. Inspired by the well-studied single unicast index coding problem (SUICP), graphical structures, similar to cycles and cliques in the side information graph of an SUICP, are identified in the side information bipartite graph of a single unicast embedded index coding problem (SUEICP). Transmission schemes based on these graphical structures, called tree cover scheme and bi-clique cover scheme are also presented for an SUEICP. Also, a relation between connectedness of the side information bipartite graph and the number of transmissions required in a scalar linear solution of an EICP is established.

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arXiv2021

Index Coded - NOMA in Vehicular Ad Hoc Networks

The demand for multimedia services is growing day by day in vehicular ad-hoc networks (VANETs), resulting in high spectral usage and network congestion. Non-orthogonal multiple access (NOMA) is a promising wireless communication technique to solve the problems related to spectral efficiency effectively. The index coding (IC) is a powerful method to improve spectral utilization, where a sender aims to satisfy the needs of multiple receivers with a minimum number of transmissions. By combining these two approaches, in this work, we propose a novel technique called index coded NOMA (IC-NOMA), where we apply NOMA techniques on index coded data to reduce the number of transmissions further. This work shows that the IC-NOMA system demands a specific design for index codes to reap the advantages of NOMA. We have done the feasibility analysis of the proposed method in a general scenario and proposed an index code design to integrate IC over NOMA for the best efficiency. Through detailed analytical studies it is validated that the proposed transmission system provides improved spectral efficiency and power saving compared to conventional IC systems.

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arXiv2021

A Secretive Coded Caching for Shared Cache Systems using PDAs

This paper considers the secretive coded caching problem with shared caches in which no user must have access to the files that it did not demand. In a shared cache network, the users are served by a smaller number of helper caches and each user is connected to exactly one helper cache. To ensure the secrecy constraint in shared cache networks, each user is required to have an individual cache of at least unit file size. For this setting, a secretive coded caching scheme was proposed recently in the literature (\enquote{Secretive Coded Caching with Shared Caches}, in \textit{IEEE Communications Letters}, 2021), and it requires a subpacketization level which is in the exponential order of the number of helper caches. By utilizing the PDA constructions, we propose a procedure to obtain new secretive coded caching schemes for shared caches with reduced subpacketization levels. We also show that the existing secretive coded caching scheme for shared caches can be recovered using our procedure. Furthermore, we derive a lower bound on the secretive transmission rate using cut-set arguments and demonstrate the order-optimality of the proposed secretive coded caching scheme.

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arXiv2021

Multi-Access Coded Caching with Demand Privacy

The demand private coded caching problem in a multi-access network with $K$ users and $K$ caches, where each user has access to $L$ neighbouring caches in a cyclic wrap-around manner, is studied. The additional constraint imposed is that one user should not get any information regarding the demands of the remaining users. A lifting construction of demand private multi-access coded caching scheme from conventional, non-private multi-access scheme is introduced. The demand-privacy for a user is ensured by placing some additional \textit{keys} in a set of caches called the \textit{private set} of that user. For a given $K$ and $L$, a technique is also devised to find the private sets of the users.

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