arXiv subjects

Avhishek Chatterjee

Publications and source records attributed to Avhishek Chatterjee.

At least 19 recordsLinked to original sources

arXiv2026

User Satisfaction-Aware Resource Allocation with Prospect-Theoretic Utility for Multimedia Streaming

Traditional resource allocation policies for multimedia streaming have primarily targeted metrics such as throughput, fairness and delay. However, user satisfaction is known to be strongly influenced by variations in throughput. Although some recent works have considered throughput variations, they overlooked a well-known aspect of human behavior that has reshaped behavioral economics over the past few decades: the same amount of decrease in throughput causes greater annoyance than the satisfaction caused by the increase. Motivated by this insight from the broad field of economics, popularly known as prospect theory, we propose a generic utility (metric) that captures both the average throughput and the asymmetric effect of throughput variations on user satisfaction. Next, we propose a resource allocation policy that reduces abrupt decreases in allocated resources when the system transitions from a resource-rich to resource-scarce state while respecting the priorities of different classes of users. Extensive simulations show that this policy outperforms the existing fair allocation policies. However, the choice of the optimal threshold depends on the network instance, which, in practice, may change frequently. Hence, building on the theoretical analysis of multi-queue systems, we propose fast numerical methods for determining the optimal threshold, which can be used in field deployments.

cs.NI↗

arXiv2026

Analytic Framework for Estimating Memory Cost

As artificial intelligence (AI) models quickly spread and become more advanced, they are requiring an ever-increasing amount of data and compute capability, leading to a significant energy cost. Training and inference of AI models including the large language models (LLMs) and deep neural networks (DNNs) are contributing to a large carbon footprint owing to the massive amount of memory they consume in data centers. In this article, we present a generalized framework that quantifies these energy costs incurred to the environment. This framework provides a foundational quantification of AI's ecological footprint, facilitating the development of sustainable architectural strategies for future models.

cs.ET↗

arXiv2026

Maximizing Qubit Throughput under Buffer Decoherence and Variability in Generation

Quantum communication networks require transmission of high-fidelity, uncoded qubits for applications such as entanglement distribution and quantum key distribution. However, current implementations are constrained by limited buffer capacity and qubit decoherence, which degrades qubit quality while waiting in the buffer. A key challenge arises from the stochastic nature of qubit generation, there exists a random delay (D) between the initiation of a generation request and the availability of the qubit. This induces a fundamental trade off early initiation increases buffer waiting time and hence decoherence, whereas delayed initiation leads to server idling and reduced throughput. We model this system as an admission control problem in a finite buffer queue, where the reward associated with each job is a decreasing function of its sojourn time. We derive analytical conditions under which a simple "no lag" policy where a new qubit is generated immediately upon the availability of buffer space is optimal. To address scenarios with unknown system parameters, we further develop a Bayesian learning framework that adaptively optimizes the admission policy. In addition to quantum communication systems, the proposed model is applicable to delay sensitive IoT sensing and service systems.

quant-ph↗

arXiv2025

Expander qLDPC Codes against Long-range Correlated Errors in Memory

Fault-tolerance using constant space-overhead against long-range correlated errors is an important practical question. In the pioneering works [Terhal and Burkard, PRA 2005], [Aliferis et al, PRA 2005], [Aharonov et al, PRL 2006], fault-tolerance using poly-logarithmic overhead against long-range correlation modeled by pairwise joint Hamiltonian was proven when the total correlation of an error at a qubit location with errors at other locations was $O(1)$, i.e., the total correlation at a location did not scale with the number of qubits. This condition, under spatial symmetry, can simply be stated as the correlation between locations decaying faster than $\frac{1}{\text{dist}^{\text{dim}}}$. However, the pairwise Hamiltonian model remained intractable for constant overhead codes. Recently, [Bagewadi and Chatterjee, PRA 2025] introduced and analyzed the generalized hidden Markov random field (MRF) model, which provably captures all stationary distributions, including long-range correlations [Kunsch et al, Ann. App. Prob. 1995]. It resulted in a noise threshold in the case of long-range correlation, for memory corrected by the linear-distance Tanner codes [Leverrier and Zemor, FOCS 2022] for super-polynomial time. In this paper, we prove a similar result for square-root distance qLDPC codes and provide an explicit expression for the noise threshold in terms of the code rate, for up to $o(\sqrt{\text{\#qubits}})$ scaling of the total correlation of error at a location with errors at other locations.

quant-ph↗

arXiv2025

Learning the Influence Graph of a Markov Process that Randomly Resets to the Past

Learning the influence graph G of a high-dimensional Markov process is central to many application domains, including social networks, neuroscience, and financial risk analysis. However, in many of these applications, future states of the process are occasionally and unpredictably influenced by a distant past state, thus destroying the Markovianity. To study this practical issue, we propose the past influence model (PIM), which captures the occasional "random resets to past" by modifying the Markovian dynamics in [1], which, in turn, is a non-linear generalization of the dynamics studied in [2], [3]. The recursive greedy algorithm proposed in this paper recovers any bounded degree $G$ when the number of ``jumps back in time" is order-wise smaller than the total number of samples, and the algorithm does not require memory.

cs.IT↗

arXiv2024

Stochastic Analysis of Retention Time of Coupled Memory Topology

Recently, it has been experimentally demonstrated that individual memory units coupled in certain topology can provide the intended performance. However, experimental or simulation based evaluation of different coupled memory topologies and materials are costly and time consuming. In this paper, inspired by Glauber dynamics models in non-equilibrium statistical mechanics, we propose a physically accurate generic mathematical framework for analyzing retention times of various coupled memory topologies and materials. We demonstrate efficacy of the proposed framework by deriving closed form expressions for a few popular coupled and uncoupled memory topologies, which match simulations. Our analysis also offers analytical insights helping us estimate the impact of materials and topologies on retention time.

cs.ET↗

arXiv2024

Limited Parallelization in Gate Operations Leads to Higher Space Overhead and Lower Noise Threshold

In a modern error corrected quantum memory or circuit, parallelization of gate operations is severely restricted due to issues like cross-talk. Hence, there are enough idle qubits not undergoing gate operations either during the computation phase or during the error correction phase, which suffer further decoherence while waiting. Thus, in reality, the space overhead and the noise threshold would depend on the level of gate parallelization. In this paper, we obtain an analytical lower bound on the required space overhead in terms of the level of parallelization for an error correction framework that has more error correction capability than the existing ones. We consider two types of errors: i.i.d. erasure and depolarization. In comparison to the known lower bounds which assume full gate parallelization, our bound is provably strictly larger despite allowing more capability to the error correction framework. This shows the steep price to be paid for lack of gate parallelization. An implication of the bound is that the noise or decoherence threshold, i.e., the noise beyond which no fault-tolerant memory or circuit can be realized, vanishes if the number of parallel gate operations does not scale linearly with the number of physical qubits.

quant-ph↗

arXiv2024

Learning Rate Optimization for Deep Neural Networks Using Lipschitz Bandits

Learning rate is a crucial parameter in training of neural networks. A properly tuned learning rate leads to faster training and higher test accuracy. In this paper, we propose a Lipschitz bandit-driven approach for tuning the learning rate of neural networks. The proposed approach is compared with the popular HyperOpt technique used extensively for hyperparameter optimization and the recently developed bandit-based algorithm BLiE. The results for multiple neural network architectures indicate that our method finds a better learning rate using a) fewer evaluations and b) lesser number of epochs per evaluation, when compared to both HyperOpt and BLiE. Thus, the proposed approach enables more efficient training of neural networks, leading to lower training time and lesser computational cost.

cs.LG↗

arXiv2024

Effect of Correlated Errors on Quantum Memory

Recent results on constant overhead LDPC code-based fault-tolerance against i.i.d. errors naturally lead to the question of fault-tolerance against errors with long-range correlations. Ideally, any correlation can be captured by a joint (system and bath) Hamiltonian. However, an arbitrary joint Hamiltonian is often intractable, and hence, the joint Hamiltonian model with pairwise terms was introduced and developed in a series of foundational works. However, the analysis of the new constant overhead codes in that error model appears to be quite challenging. In this paper, to model correlated errors in quantum memory, we introduce a correlation model which is a generalization of the well-known hidden random fields. This proposed model, which includes stationary and ergodic (non-Markov) error distributions, is shown to capture correlations not captured by the joint Hamiltonian model with pairwise terms. On the other hand, building on non-i.i.d. measure concentration, we show that for a broad class of non-Markov and (possibly) non-stationary error distributions, quantum Tanner codes ensure an exponential retention time (in the number of physical qubits), when the error rate is below a threshold. An implication of these results is that the rate of decay of the correlation with distance does not necessarily differentiate between good and bad correlation.

quant-ph↗

arXiv2024

Learning the Influence Graph of a High-Dimensional Markov Process with Memory

Motivated by multiple applications in social networks, nervous systems, and financial risk analysis, we consider the problem of learning the underlying (directed) influence graph or causal graph of a high-dimensional multivariate discrete-time Markov process with memory. At any discrete time instant, each observed variable of the multivariate process is a binary string of random length, which is parameterized by an unobservable or hidden [0,1]-valued scalar. The hidden scalars corresponding to the variables evolve according to discrete-time linear stochastic dynamics dictated by the underlying influence graph whose nodes are the variables. We extend an existing algorithm for learning i.i.d. graphical models to this Markovian setting with memory and prove that it can learn the influence graph based on the binary observations using logarithmic (in number of variables or nodes) samples when the degree of the influence graph is bounded. The crucial analytical contribution of this work is the derivation of the sample complexity result by upper and lower bounding the rate of convergence of the observed Markov process with memory to its stationary distribution in terms of the parameters of the influence graph.

cs.LG↗

arXiv2023

Dynamic Resource Allocation to Minimize Concave Costs of Shortfalls

We study a resource allocation problem over time, where a finite (random) resource needs to be distributed among a set of users at each time instant. Shortfalls in the resource allocated result in user dissatisfaction, which we model as an increasing function of the long-term average shortfall for each user. In many scenarios such as wireless multimedia streaming, renewable energy grid, or supply chain logistics, a natural choice for this cost function turns out to be concave, rather than usual convex cost functions. We consider minimizing the (normalized) cumulative cost across users. Depending on whether users' mean consumption rates are known or unknown, this problem can be reduced to two different structured non-convex problems. The "known" case is a concave minimization problem subject to a linear constraint. By exploiting a well-chosen linearization of the cost functions, we solve this provably within $\mathcal{O}\left(\frac{1}{m}\right)$ of the optimum, in $\mathcal{O}\left(m \log{m}\right)$ time, where $m$ is the number of users in the system. In the "unknown" case, we are faced with minimizing the sum of functions that are concave on part of the domain and convex on the rest, subject to a linear constraint. We present a provably exact algorithm when the cost functions and prior distributions on mean consumption are the same across all users.

math.OC↗

arXiv2023

Limits of Fault-Tolerance on Resource-Constrained Quantum Circuits for Classical Problems

Existing lower bounds on redundancy in fault-tolerant quantum circuits are applicable when both the input and the intended output are quantum states. These bounds may not necessarily hold, however, when the input and the intended output are classical bits, as in the Deutsch-Jozsa, Grover, or Shor algorithms. Here we show that indeed, noise thresholds obtained from existing bounds do not apply to a simple fault-tolerant implementation of the Deutsch-Jozsa algorithm. Then we obtain the first lower bound on the minimum required redundancy for fault-tolerant quantum circuits with classical inputs and outputs. Recent results show that due to physical resource constraints in quantum circuits, increasing redundancy can increase noise, which in turn may render many fault-tolerance schemes useless. So it is of both practical and theoretical interest to characterize the effect of resource constraints on the fundamental limits of fault-tolerant quantum circuits. Thus as an application of our lower bound, we characterize the fundamental limit of fault-tolerant quantum circuits with classical inputs and outputs under resource constraint-induced noise models.

quant-ph↗

arXiv2023

A Converse for Fault-tolerant Quantum Computation

As techniques for fault-tolerant quantum computation keep improving, it is natural to ask: what is the fundamental lower bound on redundancy? In this paper, we obtain a lower bound on the redundancy required for $ε$-accurate implementation of a large class of operations that includes unitary operators. For the practically relevant case of sub-exponential depth and sub-linear gate size, our bound on redundancy is tighter than the known lower bounds. We obtain this bound by connecting fault-tolerant computation with a set of finite blocklength quantum communication problems whose accuracy requirements satisfy a joint constraint. The lower bound on redundancy obtained here leads to a strictly smaller upper bound on the noise threshold for non-degradable noise. Our bound directly extends to the case where noise at the outputs of a gate are non-i.i.d. but noise across gates are i.i.d.

quant-ph↗

arXiv2023

Capacity Achieving Codes for an Erasure Queue-Channel

We consider a queue-channel model that captures the waiting time-dependent degradation of information bits as they wait to be transmitted. Such a scenario arises naturally in quantum communications, where quantum bits tend to decohere rapidly. Trailing the capacity results obtained recently for certain queue-channels, this paper aims to construct practical channel codes for the erasure queue-channel (EQC) -- a channel characterized by highly correlated erasures, governed by the underlying queuing dynamics. Our main contributions in this paper are twofold: (i) We propose a generic `wrapper' based on interleaving across renewal blocks of the queue to convert any capacity-achieving block code for a memoryless erasure channel to a capacity-achieving code for the EQC. Next, due to the complexity involved in implementing interleaved systems, (ii) we study the performance of LDPC and Polar codes without any interleaving. We show that standard Arıkan's Polar transform polarizes the EQC for certain restricted class of erasure probability functions. We also highlight some possible approaches and the corresponding challenges involved in proving polarization of a general EQC.

cs.IT↗

arXiv2022

Finite Time Bounds for Stochastic Bounded Confidence Dynamics

In this era of fast and large-scale opinion formation, a mathematical understanding of opinion evolution, a.k.a. opinion dynamics, acquires importance. Linear graph-based dynamics and bounded confidence dynamics are the two popular models for opinion dynamics in social networks. Stochastic bounded confidence (SBC) opinion dynamics was proposed as a general framework that incorporates both these dynamics as special cases and also captures the inherent stochasticity and noise (errors) in real-life social exchanges. Although SBC dynamics is quite general and realistic, its analysis is more challenging. This is because SBC dynamics is nonlinear and stochastic, and belongs to the class of Markov processes that have asymptotically zero drift and unbounded jumps. The asymptotic behavior of SBC dynamics was characterized in prior works. However, they do not shed light on its finite-time behavior, which is often of interest in practice. We take a stride in this direction by analyzing the finite-time behavior of a two-agent system and a bistar graph, which are crucial to the understanding of general multi-agent dynamics. In particular, we show that the opinion difference between the two agents is well-concentrated around zero under the conditions that lead to asymptotic stability of the SBC dynamics.

cs.SI↗

arXiv2022

Towards Maximizing Nonlinear Delay Sensitive Rewards in Queuing Systems

We consider maximizing the long-term average reward in a single server queue, where the reward obtained for a job is a non-increasing function of its sojourn time. The motivation behind this work comes from multiple applications, including quantum information processing and multimedia streaming. We introduce a new service discipline, shortest predicted sojourn time (SPST), which, in simulations, performs better than well-known disciplines. We also present some limited analytical guarantees for this highly intricate problem.

cs.PF↗

arXiv2022

Unital Qubit Queue-channels: Classical Capacity and Product Decoding

Quantum queue-channels arise naturally in the context of buffering in quantum networks, wherein the noise suffered by the quantum states depends on the time spent waiting in the buffer. It has been shown that the upper-bound on the classical capacity of an additive queue-channel has a simple expression, and is achievable for the erasure and depolarizing channels [IEEE JSAIT, 1(2):432-444]. In this paper, we characterise the classical capacity for the class of unital qubit queue-channels, and show that a simple product (non-entangled) decoding strategy is capacity-achieving. As an intermediate result, we derive an explicit capacity achieving product decoding strategy for any i.i.d. unital qubit channel, which could be of independent interest. As an important special case, we also derive the capacity and optimal decoding strategies for a symmetric generalized amplitude damping (GAD) queue-channel. Our results provide useful insights towards designing practical quantum communication networks, and highlight the need to explicitly model the impact of buffering.

quant-ph↗

arXiv2022

Multi-channel Resource Allocation for Smooth Streaming: Non-convexity and Bandits

User dissatisfaction due to buffering pauses during streaming is a significant cost to the system, which we model as a non-decreasing function of the frequency of buffering pause. Minimization of total user dissatisfaction in a multi-channel cellular network leads to a non-convex problem. Utilizing a combinatorial structure in this problem, we first propose a polynomial time joint admission control and channel allocation algorithm which is provably (almost) optimal. This scheme assumes that the base station (BS) knows the frame statistics of the streams. In a more practical setting, where these statistics are not available a priori at the BS, a learning based scheme with provable guarantees is developed. This learning based scheme has relation to regret minimization in multi-armed bandits with non-i.i.d. and delayed reward (cost). All these algorithms require none to minimal feedback from the user equipment to the base station regarding the states of the media player buffer at the application layer, and hence, are of practical interest.

cs.NI↗