arXiv subjects

B. Sundar Rajan

Publications and source records attributed to B. Sundar Rajan.

At least 37 records · Page 2Linked to original sources

arXiv2025

On Hierarchical Coded Caching with Offline Users

This paper studies a two-layer hierarchical network in which some users are offline during the content delivery phase. A two-layer hierarchical network consists of a single server connected to multiple cache-aided mirror sites, and each mirror site is connected to a distinct set of cache-aided users. A scheme for such a hierarchical system with offline users has been proposed recently but considered a special case where all mirror caches have zero memory, which is a significant limitation. We propose an array known as a hierarchical hotplug placement delivery array (HHPDA), which describes the placement and delivery phases of a coded caching scheme for a general two-layer hierarchical network with offline users. Further, we construct a class of HHPDAs using combinatorial t-designs.

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arXiv2025

Combinatorial Multi-Access Coded Caching with Private Caches under Intersecting Index Constraints

We consider the coded caching system where each user, equipped with a private cache, accesses a distinct r-subset of access caches. A central server housing a library of files populates both private and access caches using uncoded placement. In this work, we focus on a constrained indexing regime, referred to as the intersection class, in which the sets used to index the demands of each user must have a nonempty intersection. This regime models resource-limited IoT scenarios such as edge-assisted IoT systems, where devices with small private caches connect to a small number of shared caches. We provide a necessary and sufficient condition under which the system parameters fall within this intersection class. Under this condition, we propose a centralized coded caching scheme and characterize its rate-memory trade-off. Next, we define a uniform-intersection subclass and establish a condition under which the system belongs to this subclass. Within this subclass, the proposed scheme has a regular structure, with each transmission benefiting the same number of users, and we characterize its rate-memory trade-off. Additionally, we derive an index coding-based lower bound on the minimum achievable worst-case rate under uncoded placement. Finally, we provide numerical comparisons between the rate of the proposed scheme, the new lower bound, and bounds from the original work.

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arXiv2025

On Function-Correcting Codes

Function-correcting codes were introduced in the work "Function-Correcting Codes" (FCC) by Lenz et al. 2023, which provides a graphical representation for the problem of constructing function-correcting codes. We use this function dependent graph to get a lower bound on the redundancy required for function correction codes. By considering the function to be a bijection, such an approach leads to a lower bound on the redundancy required for classical systematic error correcting codes (ECCs). We propose a range of parameters for which the bound is tight. For single error correcting codes, we show that this bound is at least as good as a bound proposed by Zinoviev, Litsyn, and Laihonen in 1998. Thus, this framework helps to study systematic classical error correcting codes. Further, we study the structure of this function dependent graph for linear functions, which leads to bounds on the redundancy of linear-function correcting codes. We show that the Plotkin-like bound for function-correcting codes proposed by Lenz et.al 2023 is simplified for linear functions. We identify a class of linear functions for which an upper bound proposed by Lenz et al., is tight and also identify a class of functions for which coset-wise coding is equivalent to a lower dimensional classical error correction problem.

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arXiv2025

Hierarchical Coded Caching with Low Subpacketization and Coding Delay using Combinatorial t-Designs

Coded caching scheme originally proposed by Maddah-Ali and Niesen (MN) considered a broadcast network consisting of a single server connected to a set of users each having a cache memory. Motivated by practical scenarios, Karamchandani \textit{et al.} in [16] proposed a coded caching scheme for a two-layer hierarchical network consisting of a single server connected to multiple mirror sites and each mirror site connected to a distinct set of users, in which both mirror sites and users having cache memories. Low subpacketization level coded caching schemes are desirable for practical implementations. Placement delivery array (PDA) was proposed as a tool to design coded caching schemes with reduced subpacketization level by Yan \textit{et al.} in [4]. Schemes with reduced subpacketization levels are studied extensively in the literature for single-layer networks. Kong \textit{et al.} in [17] proposed a structure called hierarchical placement delivery arrays (HPDA), which characterizes a hierarchical coded caching system and also proposed a class of HPDAs that gives low subpacketization level schemes by using two PDAs. Low subpacketization level hierarchical schemes using combinatorial $t$-designs is proposed in [20]. Apart from that there is no other existing work that discusses the subpacketization problem in a hierarchical network. This paper proposes a class of HPDA construction that gives low subpacketization level hierarchical coded caching schemes, by first constructing a new class of PDAs. Compared with the existing schemes, in cases where the system parameters and subpacketization level are the same, the proposed hierarchical scheme has a better coding delay. Further, the new class of PDAs constructed either subsumes several known PDA constructions or achieves better transmission load for the same system parameters.

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arXiv2025

Secrecy and Privacy in Multi-Access Combinatorial Topology

In this work, we consider the multi-access combinatorial topology with $C$ caches where each user accesses a unique set of $r$ caches. For this setup, we consider secrecy, where each user should not know anything about the files it did not request, and demand privacy, where each user's demand must be kept private from other non-colluding users. We propose a scheme satisfying both conditions and derive a lower bound based on cut-set arguments. Also, we prove that our scheme is optimal when $r\geq C-1$, and it is order-optimal when the cache memory size $M$ is greater than or equal to a certain threshold for $r<C-1$. When $r=1$, in most of the memory region, our scheme achieves the same rate as the one given by the secretive scheme for the dedicated cache setup by Ravindrakumar et al. ( 'Private Coded Caching,' in \textit{IEEE Transactions on Information Forensics and Security}, 2018), while satisfying both secrecy and demand privacy conditions.

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arXiv2025

A Note on Function Correcting Codes for b-Symbol Read Channels

Function-Correcting Codes (FCCs) is a novel paradigm in Error Control Coding introduced by Lenz et. al. 2023 for the binary substitution channel \cite{FCC}. FCCs aim to protect the function evaluation of data against errors instead of the data itself, thereby relaxing the redundancy requirements of the code. Later R. Premlal et. al. \cite{LFCC} gave new bounds on the optimal redundancy of FCCs and also extensively studied FCCs for linear functions. The notion of FCCs has also been extended to different channels such as symbol-pair read channel over the binary field by Xia et. al. \cite{FCSPC} and b-symbol read channel over finite fields by A.Singh et. al. \cite{FCBSC} In this work, we study FCCs for linear functions for the b-symbol read channel. We provide the Plotkin-like bound on FCCs for b-symbol read channel which reduces to a Plotkin-like bound for FCCs for the symbol-pair read channel when $b$=2. FCCs reduce to classical Error Correcting Codes (ECCs) when the function is bijective. Analogous to this our bound reduces to the Plotkin-bound for classical ECCS for both the b-symbol and symbol-pair read channels \cite{Plotkin-b-symbol, Plotkin-symbol-pair} when we consider linear bijective functions.

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arXiv2025

Multi-Antenna Coded Caching for Multi-Access Networks with Cyclic Wrap-Around

This work explores a multiple transmit antenna setting in a multi-access coded caching (MACC) network where each user accesses more than one cache. A MACC network has $K$ users and $K$ caches, and each user has access to $r < K$ consecutive caches in a cyclic wrap-around manner. There are $L$ antennas at the server, and each cache has a normalized size of $M/N \leq 1$. The cyclic wrap-around MACC network with a single antenna at the server has been a well-investigated topic, and several coded caching schemes and improved lower bounds on the performance are known for the same. However, this MACC network has not yet been studied under multi-antenna settings in the coded caching literature. We study the multi-antenna MACC problem and propose a solution for the same by constructing a pair of arrays called caching and delivery arrays. We present three constructions of caching and delivery arrays for different scenarios and obtain corresponding multi-antenna MACC schemes for the same. Two schemes resulting from the above constructions achieve optimal performance under uncoded placement and one-shot delivery. The optimality is shown by matching the performance of the multi-antenna MACC scheme to that of an optimal multi-antenna scheme for a dedicated cache network having an identical number of users, and each user has a normalized cache size of $rM/N$. Further, as a special case, one of the proposed schemes subsumes an existing optimal MACC scheme for the single-antenna setting.

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arXiv2025

Hierarchical Coded Caching in High Memory Regime with Coded Placement

We consider a two-layer hierarchical coded caching network where a server with a library of $N$ files is connected to $K_1$ mirrors, each having a cache memory of size $M_1$. Each mirror is further connected to $K_2$ users, each equipped with a dedicated cache of size $M_2$. In this paper, we propose two distinct coded caching schemes based on coded placement, corresponding to two distinct memory pairs, $ (M_1, M_2) $. We show that the proposed schemes outperform the existing schemes at these memory points given by the proposed schemes for smaller values of $K_2$. In setups where mirrors are positioned near each other, avoiding signal interference is crucial. This can be ensured by having all mirrors transmit using orthogonal carrier frequencies. To compare our schemes with existing ones, we used the composite rate metric, which accurately represents the total bandwidth utilized in such setups. The composite rate is given by $\overline{R} = R_1 + K_1 R_2$, where $R_1$ is the rate from the server to the mirrors, and $R_2$ is the rate from the mirrors to the users, with respect to $M_1$ and $M_2$.

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arXiv2025

Coded Caching for Hierarchical Two-Layer Networks with Coded Placement

We examine a two-layered hierarchical coded caching problem, a configuration addressed in existing research. This involves a server connected to $K_1$ mirrors, each of which serves $K_2$ users. The mirrors and the users are equipped with caches of size $M_1$ and $M_2$, respectively. We propose a hierarchical coded caching scheme with coded placements that outperforms existing schemes. To ensure a fair comparison, we introduce the notion of composite rate, defined as $\overline{R} = R_1 + K_1 R_2$, where $R_1$ is the rate from the server to mirrors and $R_2$ is the rate from mirrors to users. The composite rate has not been discussed before in the literature and is pertinent when mirrors transmit with different carrier frequencies. For the proposed scheme, we show a trade-off between the global memory $\overline{M}=K_1M_1+K_1K_2M_2$ of the system and the composite rate and compare with the existing schemes. Additionally, we conduct this comparative analysis by plotting $R_1$ + $R_2$ against global memory, which is particularly beneficial for systems wherein each mirror can utilize the same carrier frequency, given their significant spatial separation. Additionally, we propose an optimized scheme for the specific case of a single mirror, showing improved performance in this scenario.

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arXiv2024

Cyclic Wrap-Around Multi-Access Coded Caching with Private Caches

We consider a variant of the coded caching problem where users connect to two types of caches, called private caches and access caches. The problem setting consists of a server having a library of files and a set of access caches. Every user, equipped with a private cache, connects to $L$ neighboring access caches in a cyclic wrap-around fashion. The server populates the private and access caches with file contents in either coded or uncoded format. For this setting, we derive a lower bound on the optimal worst-case transmission rate using cut-set arguments. This lower bound applies to both coded and uncoded placements. We then provide an achievable scheme with uncoded placement and show that our scheme specializes to the well-known Maddah-Ali-Niesen scheme for the dedicated cache network in the absence of access caches. Finally, we show that the proposed scheme achieves optimality in large memory regimes and provide numerical plots comparing the rate of the proposed scheme with the derived lower bound, demonstrating the optimality of our scheme.

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arXiv2024

Average Probability of Error for Single Uniprior Index Coding over Rayleigh Fading Channel

Ong and Ho developed optimal linear index codes for single uniprior index coding problems (ICPs) by finding a spanning tree for each of the strongly connected components of the corresponding information-flow graphs, following which Thomas et al. considered the same class of ICPs over Rayleigh fading channel. They developed the min-max probability of error criterion for choosing an index code which minimized the probability of error at the receivers and showed that there always exist optimal linear index codes for which any receiver takes at most two transmissions to decode a requested message. Motivated by the above works, this paper considers single uniprior ICPs over Rayleigh fading channels for which minimizing average probability of error is shown to be a criterion for further selection of index codes. The optimal index code w.r.t this criterion is shown to be one that minimizes the total number of transmissions used for decoding the message requests at all the receivers. An algorithm that generates a spanning tree which has a lower value of this metric as compared to the optimal star graph is also presented. For a given set of parameters of single uniprior ICPs, a lower bound for the total number of transmissions used by any optimal index code is derived, and a class of ICPs for which this bound is tight is identified.

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arXiv2024

Combinatorial Multi-Access Coded Caching with Private Caches

We consider a variant of the coded caching problem where users connect to two types of caches, called private and access caches. The problem setting consists of a server with a library of files and a set of access caches. Each user, equipped with a private cache, connects to a distinct $r-$subset of the access caches. The server populates both types of caches with files in uncoded format. For this setting, we provide an achievable scheme and derive a lower bound on the number of transmissions for this scheme. We also present a lower and upper bound for the optimal worst-case rate under uncoded placement for this setting using the rates of the Maddah-Ali--Niesen scheme for dedicated and combinatorial multi-access coded caching settings, respectively. Further, we derive a lower bound on the optimal worst-case rate for any general placement policy using cut-set arguments. We also provide numerical plots comparing the rate of the proposed achievability scheme with the above bounds, from which it can be observed that the proposed scheme approaches the lower bound when the amount of memory accessed by a user is large. Finally, we discuss the optimality w.r.t worst-case rate when the system has four access caches.

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arXiv2024

An Optimal Decentralized Multi-access Coded Caching System

In this paper, we consider a multi-access coded caching system with decentralized prefetching, where a server hosts $N$ files, each of size $F$ bits, and is connected to $K$ users through a shared link. There are $c$ caches distributed across the network and each of the $K$ users connects to a random set of $r\leq c$ caches. Initially, we consider the model in which each of the cache subsets is accessed by exactly a specific number of users. For this model, a novel linear delivery scheme is introduced, using which the closed-form expression for the per-user delivery rate is computed. Furthermore, using techniques from index coding, the optimality of the proposed linear delivery scheme among all linear delivery schemes is proved. The results of the decentralized shared caching and conventional decentralized caching schemes are recovered as special cases of the proposed model. The model is further generalized by allowing each cache subset to serve any number of users. This enhances the flexibility of the system, enabling it to accommodate any arbitrary number of users. A delivery scheme is proposed for the generalized model and is shown to be optimal for certain user-to-cache associations.

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arXiv2024

Wireless MapReduce Arrays for Coded Distributed Computing

We consider a wireless distributed computing system based on the MapReduce framework, which consists of three phases: \textit{Map}, \textit{Shuffle}, and \textit{Reduce}. The system consists of a set of distributed nodes assigned to compute arbitrary output functions depending on a file library. The computation of the output functions is decomposed into Map and Reduce functions, and the Shuffle phase, which involves the data exchange, links the two. In our model, the Shuffle phase communication happens over a full-duplex wireless interference channel. For this setting, a coded wireless MapReduce distributed computing scheme exists in the literature, achieving optimal performance under one-shot linear schemes. However, the scheme requires the number of input files to be very large, growing exponentially with the number of nodes. We present schemes that require the number of files to be in the order of the number of nodes and achieve the same performance as the existing scheme. The schemes are obtained by designing a structure called wireless MapReduce array that succinctly represents all three phases in a single array. The wireless MapReduce arrays can also be obtained from the extended placement delivery arrays known for multi-antenna coded caching schemes.

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arXiv2024

Two-Dimensional Multi-Access Coded Caching with Multiple Transmit Antennas

This work introduces a multi-antenna coded caching problem in a two-dimensional multi-access network, where a server with $L$ transmit antennas and $N$ files communicates to $K_1K_2$ users, each with a single receive antenna, through a wireless broadcast link. The network consists of $K_1K_2$ cache nodes and $K_1K_2$ users. The cache nodes, each with capacity $M$, are placed on a rectangular grid with $K_1$ rows and $K_2$ columns, and the users are placed regularly on the square grid such that a user can access $r^2$ neighbouring caches in a cyclic wrap-around fashion. For a given cache memory $M$, the goal of the coded caching problem is to serve the user demands with a minimum delivery time. We propose a solution for the aforementioned coded caching problem by designing two arrays: a caching array and a delivery array. Further, we present two classes of caching and delivery arrays and obtain corresponding multi-access coded caching schemes. The first scheme achieves a normalized delivery time (NDT) $\frac{K_1K_2(1-r^2\frac{M}{N})}{L+K_1K_2\frac{M}{N}}$. The second scheme achieves an NDT $\frac{K_1K_2(1-r^2\frac{M}{N})}{L+K_1K_2r^2\frac{M}{N}}$ when $M/N=1/K_1K_2$ and $L=K_1K_2-r^2$, which is optimal under uncoded placement and one-shot delivery.

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arXiv2024

Placement Delivery Arrays for Coded Caching with Shared and Private Caches

We consider a coded caching network consisting of a server with a library of $N$ files connected to $K$ users, where each user is equipped with a dedicated cache of size $M_p$ units. In addition to that, the network consists of $Λ\leq K$ helper caches, each with a size $M_h$ units. Each helper cache can serve an arbitrary number of users; however, each user can access only a single helper cache. Also, we assume that the server knows the user-to-helper cache association, defined as the sets of users connected to each helper cache, during the cache placement phase. We propose a solution for the aforementioned coded caching problem by introducing a combinatorial structure called a Shared and Private Placement Delivery Array (SP-PDA). These SP-PDAs describe the helper cache placement, private cache placement, and the server transmissions in a single array. Further, we propose a novel construction of SP-PDAs using two Placement Delivery Arrays (PDAs). Interestingly, we observe that the permutations of the columns of the two chosen PDAs result in SP-PDAs with different performances. Moreover, we characterize the conditions for selecting the best column permutations of the chosen PDAs. Furthermore, the coded caching schemes resulting from SP-PDAs subsume two existing coded caching schemes as special cases. Additionally, SP-PDAs enable the construction of coded caching schemes with much smaller subpacketization numbers -subpacketization number is defined as the number of subfiles to which a file is divided- compared to the existing schemes, without paying much in terms of rate (the size of the transmission in the delivery phase).

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arXiv2024

Single-Server Pliable Private Information Retrieval with Identifiable Side Information

In Pliable Private Information Retrieval (PPIR) with a single server, messages are partitioned into $Γ$ non-overlapping classes. The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. In S. A. Obead, H. Y. Lin and E. Rosnes, Single-Server Pliable Private Information Retrieval With Side Information, arXiv:2305.06857, authors consider the problem of PPIR with Side Information (PPIR-SI), where the user now has side information. The user wants to retrieve any new message (not included in the side information) from its desired class without revealing the identity of the desired class and its side information. A scheme for the PPIR-SI is given by Obead et al. for the case when the users side information is unidentified, and this case is referred to as PPIR with Unidentifiable SI (PPIR-USI). In this paper, we study the problem of PPIR for the single server case when the side information is partially identifiable, and we term this case as PPIR with Identifiable Side Information (PPIR-ISI). The user is well aware of the identity of the side information belonging to $η$ number of classes, where $1\leq η\leq Γ$. In this problem, The user wants to retrieve a message from its desired class without revealing the identity of the desired class to the server. We give a scheme for PPIR-ISI, and we prove that having identifiable side information is advantageous by comparing the rate of the proposed scheme to the rate of the PPIR-USI scheme given by Obead et al. for some cases. Further, we extend the problem of PPIR-ISI for multi-user case, where users can collaborately generate the query sets, and we give a scheme for this problem.

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arXiv2024

A New Hotplug Coded Caching Scheme Using PDAs

In the original coded caching model introduced by Maddah-Ali and Niesen in 2014, the server starts broadcasting only after it receives demands from all the users. So, all the users must be active during the delivery phase. In this work, we consider a coded caching model called hotplug coded caching in which some of the users are offline during the delivery phase. This model was first introduced by Ma and Tuninetti (``On Coded Caching Systems with Offline Users," 2022 IEEE International Symposium on Information Theory). The concept of Hotplug Placement Delivery Arrays (HpPDAs) for the hotplug coded caching systems was introduced in (``Improved Hotplug Caching Schemes Using PDAs and $t$-Designs," \emph{arXiv:2311.02856}, 2024), in which the authors have constructed HpPDAs from $t$-designs. This work provides a new hotplug coded caching scheme from the existing HpPDAs. The performance comparison of the proposed scheme with the existing schemes is presented. When applied for HpPDAs from $t$-designs, our scheme outperforms the baseline scheme by Ma and Tuninetti, and the Improved $t$-scheme by Rajput and Rajan in some memory regimes.

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