arXiv subjects

Arun Padakandla

Publications and source records attributed to Arun Padakandla.

At least 19 recordsLinked to original sources

arXiv2026

An Achievable Rate Region for 3-User Classical Quantum Broadcast Channel via Coset Codes

We undertake a Shannon theoretic study of the problem of communicating statistically independent bit streams over a 3-user classical quantum broadcast channel (3-CQBC) and focus on characterizing inner bounds to its capacity region. We propose a coding strategy based on coset codes possessing algebraic closure properties. Elevating Sen's technique of tilting, smoothing, and augmentation - originally designed only for IID codes - we design new POVMs that can simultaneously decode into a combination of unstructured IID and coset codes to efficiently decode univariate and bivariate interferences respectively. Analyzing the information-theoretic performance of the proposed coding strategy we characterize a new inner bound to the capacity region of the 3-CQBC that subsumes all currently known bounds and is proven to be strictly larger for identified examples.

cs.IT↗

arXiv2026

Simultaneous Decoding of Classical Coset Codes over 3-User Quantum Interference Channel : New Achievable Rate Regions

We undertake a Shannon theoretic study of the problem of communicating bit streams over a 3-user classical-quantum interference channel (3-CQIC) and focus on characterizing inner bounds. We design a new coding strategy based on (i) coset codes possessing algebraic closure properties and (ii) decoding POVMs to decode bi-variate interference efficiently. Needing to perform simultaneous decoding, we enhance Sen's powerful technique of tilting, smoothing, and augmentation - originally designed only for IID codes - to decode into `functions of codebooks'. Developing analysis techniques to combine all of these elements, we derive a new inner bound to the capacity region of a 3-CQIC. The derived inner bound subsumes all currently known inner bounds and is analytically proven to be strictly larger for identified examples, including non-commutative `additive' and `non-additive' ones.

cs.IT↗

arXiv2026

Distributed Instrument Simulation with Quantum Side Information in the One-Shot Regime

Three distributed parties, two transmitters (Txs) and a receiver (Rx), hold one component each of a tripartite quantum state $ρ^{A_1A_2C}$. The goal is to simulate the action of a separable instrument acting on the $A_1$ and $A_2$ components, with the Rx recovering the classical outcome. To enable this, each Tx $k$ can transfer bits on a noiseless bit pipe and share randomness at rates $R_k$ and $C_k$, respectively, with the Rx. Undertaking a Shannon-theoretic study, we characterize two new sets of inner bounds. The first set, derived for the one-shot regime, is based on instrument simulation protocols built using unstructured IID codes, while the second set, derived for the asymptotic regime, relies on coset codes and new decoding POVMs. The first set of bounds recovers current known inner bounds for instrument and measurement simulation in all previously studied scenarios. Our protocols are based on likelihood POVMs, and our analysis leverages Sen's smooth multiparty covering and simultaneous decoding, while handling the distributed-component scenario via a compatible operator sliding trick.

quant-ph↗

arXiv2026

Rate Loss in Quantum Channels with Classical State and Applications for Quantum Broadcast Channels

We consider the problem of \textit{rate loss} - a strict penalty suffered in achievable rates due to the lack of channel state information at the receiver (Rx) of a classical-quantum (CQ) channel. First, we identify non-commutative CQ channels and analytically prove a rate loss. Building on this, we next prove that coset-code-based strategies can strictly outperform conventional unstructured IID-code-based strategies for non-commutative 3-user CQ broadcast channels.

cs.IT↗

arXiv2025

An Achievable Rate Region for $3-$User Classical-Quantum Broadcast Channels

We consider the scenario of communicating on a $3\mhyphen$user classical-quantum broadcast channel. We undertake an information theoretic study and focus on the problem of characterizing an inner bound to its capacity region. We design a new coding scheme based \textit{partitioned coset codes} - an ensemble of codes possessing algebraic properties. Analyzing its information-theoretic performance, we characterize a new inner bound. We identify examples for which the derived inner bound is strictly larger than that achievable using IID random codes. Proceeding further, we incorporate Sen's technique of tilting smoothing and augmentation to perform simultaneous decoding via a simultaneous decoding POVM and thereby characterize a further enlarged achievable rate region for communicating classical bits over the $3-$user classical-quantum broadcast channel. Finally, in our last step, we characterize a new inner bound to the classical-quantum capacity region of the $3-$user classical-quantum broadcast channel that subsumes all previous known inner bounds by combining the conventional unstructured IID codes with structured coset code strategies.

cs.IT↗

arXiv2023

Fat Shattering, Joint Measurability, and PAC Learnability of POVM Hypothesis Classes

We characterize learnability for quantum measurement classes by establishing matching necessary and sufficient conditions for their PAC learnability, along with corresponding sample complexity bounds, in the setting where the learner is given access only to prepared quantum states. We first probe the results from previous works on this setting. We show that the empirical risk defined in previous works and matching the definition in the classical theory fails to satisfy the uniform convergence property enjoyed in the classical setting for some learnable classes. Moreover, we show that VC dimension generalization upper bounds in previous work are frequently infinite, even for finite-dimensional POVM classes. To surmount the failure of the standard ERM to satisfy uniform convergence, we define a new learning rule -- denoised ERM. We show this to be a universal learning rule for POVM and probabilistically observed concept classes, and the condition for it to satisfy uniform convergence is finite fat shattering dimension of the class. We give quantitative sample complexity upper and lower bounds for learnability in terms of finite fat-shattering dimension and a notion of approximate finite partitionability into approximately jointly measurable subsets, which allow for sample reuse. We then show that finite fat shattering dimension implies finite coverability by approximately jointly measurable subsets, leading to our matching conditions. We also show that every measurement class defined on a finite-dimensional Hilbert space is PAC learnable. We illustrate our results on several example POVM classes.

stat.ML↗

arXiv2022

Centralised multi link measurement compression with side information

We prove new one shot achievability results for measurement compression of quantum instruments with side information at the receiver. Unlike previous one shot results for this problem, our one shot bounds are nearly optimal and do not need catalytic randomness. In fact, we state a more general problem called centralised multi link measurement compression with quantum side information and provide one shot achievability results for it. As a simple corollary, we obtain one shot measurement compression results for quantum instruments with side information that we mentioned earlier. All our one shot results lead to the standard results for this problem in the asymptotic iid setting. We prove our achievability bounds by first proving a novel sequential classical quantum multipartite covering lemma, which should be of independent interest.

quant-ph↗

arXiv2022

Communicating over a Classical-Quantum MAC with State Information Distributed at Senders

We consider the problem of communicating over a classical-quantum (CQ) multiple access channel with random classical states non-causally available at the transmitter, referred to as a QMSTx. QMSTx is a classical-quantum multiple access analogue of the channel considered by Gelfand and Pinsker in 1980. We undertake a Shannon-theoretic study and focus on the problem of characterizing inner bounds to the capacity region of a QMSTx. We propose a new coding scheme based on \textit{union coset codes} - codes possessing algebraic properties and derive a new inner bound that subsumes the inner based on IID random coding. We identify examples for which the derived inner bound is strictly larger.

cs.IT↗

arXiv2022

Unified approach for computing sum of sources over CQ-MAC

We consider the task of communicating a generic bivariate function of two classical sources over a Classical-Quantum Multiple Access Channel (CQ-MAC). The two sources are observed at the encoders of the CQ-MAC, and the decoder aims at reconstructing a bivariate function from the received quantum state. Inspired by the techniques developed for the analogous classical setting, and employing the technique of simultaneous (joint) decoding developed for the classical-quantum setting, we propose and analyze a coding scheme based on a fusion of algebraic structured and unstructured codes. This coding scheme allows exploiting both the symmetric structure common amongst the sources and the asymmetries. We derive a new set of sufficient conditions that strictly enlarges the largest known set of sources (capable of communicating the bivariate function) for any given CQ-MAC. We provide these conditions in terms of single-letter quantum information-theoretic quantities.

cs.IT↗

arXiv2021

A Theoretical Framework for Learning from Quantum Data

Over decades traditional information theory of source and channel coding advances toward learning and effective extraction of information from data. We propose to go one step further and offer a theoretical foundation for learning classical patterns from quantum data. However, there are several roadblocks to lay the groundwork for such a generalization. First, classical data must be replaced by a density operator over a Hilbert space. Hence, deviated from problems such as state tomography, our samples are i.i.d density operators. The second challenge is even more profound since we must realize that our only interaction with a quantum state is through a measurement which -- due to no-cloning quantum postulate -- loses information after measuring it. With this in mind, we present a quantum counterpart of the well-known PAC framework. Based on that, we propose a quantum analogous of the ERM algorithm for learning measurement hypothesis classes. Then, we establish upper bounds on the quantum sample complexity quantum concept classes.

quant-ph↗

arXiv2021

Source Coding for Synthesizing Correlated Randomness

We consider a scenario wherein two parties Alice and Bob are provided $X_{1}^{n}$ and $X_{2}^{n}$ -- samples that are IID from a PMF $P_{X_1 X_2}$. Alice and Bob can communicate to Charles over (noiseless) communication links of rate $R_1$ and $R_2$ respectively. Their goal is to enable Charles generate samples $Y^{n}$ such that the triple $(X_{1}^{n},X_{2}^{n},Y^{n})$ has a PMF that is close, in total variation, to $\prod P_{X_1 X_2 Y}$. In addition, the three parties may posses pairwise shared common randomness at rates $C_1$ and $C_2$. We address the problem of characterizing the set of rate quadruples $(R_1,R_2,C_1,C_2)$ for which the above goal can be accomplished. We provide a set of sufficient conditions, i.e. an inner bound to the achievable rate region, and necessary conditions, i.e. an outer bound to the rate region for this three party setup. We provide a joint-typicality based random coding argument involving encoding and decoding operations to perform soft covering and a pertinent relaxation of the PMF requirement for the encoders.

cs.IT↗

arXiv2021

Synthesizing Correlated Randomness using Algebraic Structured Codes

In this problem, Alice and Bob, are provided $X_{1}^{n}$ and $X_{2}^{n}$ that are IID $p_{X_1 X_2}$. Alice and Bob can communicate to Charles over (noiseless) links of rate $R_1$ and $R_2$, respectively. Their goal is to enable Charles generate samples $Y^{n}$ such that the triple $(X_{1}^{n},X_{2}^{n},Y^{n})$ has a PMF that is close, in total variation, to $\prod p_{X_1 X_2 Y}$. In addition, the three parties may posses shared common randomness at rate $C$. We address the problem of characterizing the set of rate triples $(R_1,R_2,C)$ for which the above goal can be accomplished. We build on our recent findings and propose a new coding scheme based on coset codes. We analyze its information-theoretic performance and derive a new inner bound. We identify examples for which the derived inner bound is analytically proven to contain rate triples that are not achievable via any known unstructured code based coding techniques. Our findings build on a variant of soft-covering which generalizes its applicability to the algebraic structured code ensembles. This adds to the advancement of the use structured codes in network information theory.

cs.IT↗

arXiv2021

Achievable rate-region for $3-$User Classical-Quantum Interference Channel using Structured Codes

We consider the problem of characterizing an inner bound to the capacity region of a $3-$user classical-quantum interference channel ($3-$CQIC). The best known coding scheme for communicating over CQICs is based on unstructured random codes and employs the techniques of message splitting and superposition coding. For classical $3-$user interference channels (ICs), it has been proven that coding techniques based on coset codes - codes possessing algebraic closure properties - strictly outperform all coding techniques based on unstructured codes. In this work, we develop analogous techniques based on coset codes for $3$to$1-$CQICs - a subclass of $3-$user CQICs. We analyze its performance and derive a new inner bound to the capacity region of $3$to$1-$CQICs that subsume the current known largest and strictly enlarges the same for identified examples.

cs.IT↗

arXiv2021

Computing Sum of Sources over a Classical-Quantum MAC

We consider the problem of communicating a general bivariate function of two classical sources observed at the encoders of a classical-quantum multiple access channel. Building on the techniques developed for the case of a classical channel, we propose and analyze a coding scheme based on coset codes. The proposed technique enables the decoder recover the desired function without recovering the sources themselves. We derive a new set of sufficient conditions that are weaker than the current known for identified examples. This work is based on a new ensemble of coset codes that are proven to achieve the capacity of a classical-quantum point-to-point channel.

cs.IT↗

arXiv2019

Communicating Correlated Sources over MAC and Interference Channels I : Separation-based schemes

We consider the two scenarios of communicating a pair $S_{1},S_{2}$ of correlated sources over multiple access (MAC) and interference channels (IC) respectively. We undertake a Shannon theoretic study and focus on achievability, i.e., characterizing sufficient conditions. In the absence of a Gaćs-Körner-Witsenhausen common part, the current known single-letter (S-L) coding schemes are constrained to the S-L long Markov Chain (LMC) $X_{1}-S_{1}-S_{2}-X_{2}$. Taking the lead of Dueck's example [Dueck, Mar 1981], we recognize that the latter constraint is debilitating, leading to sub-optimality of S-L coding schemes. The goal of our work is to design a coding scheme wherein (i) the choice of channel input at time $t$ is based on multiple source symbols, and is yet ii) amenable to performance characterization via S-L expressions. In this article, we present the first part of our findings. We propose a new separation-based coding scheme based on a fixed block-length (B-L) codes that enables choice of $X_{jt}$ - the symbol input on the channel by encoder $j$ at time $t$ - to be based on a generic number $l$ of source symbols $S_{j}^{l}$, thus permitting correlation of the input symbols $X_{1},X_{2}$ through a multi-letter LMC $X_{1}-S_{1}^{l}-S_{2}^{l}-X_{2}$. By carefully stitching together S-L coding techniques we devise a multi-letter coding scheme. We characterize an inner bound to its performance via a S-L expression and prove that the derived inner bound is strictly larger than the current known largest inner bounds for both the MAC and IC problems based on S-L coding schemes. In the second part of our work, we propose to enlarge the inner bound derived in this article by incorporating the technique of inducing source correlation onto channel inputs [Cover, El Gamal and Salehi, Nov 1980].

cs.IT↗

arXiv2018

The Trade-off between Privacy and Fidelity via Ehrhart Theory

As an increasing amount of data is gathered nowadays and stored in databases (DBs), the question arises of how to protect the privacy of individual records in a DB even while providing accurate answers to queries on the DB. Differential Privacy (DP) has gained acceptance as a framework to quantify vulnerability of algorithms to privacy breaches. We consider the problem of how to sanitize an entire DB via a DP mechanism, on which unlimited further querying is performed. While protecting privacy, it is important that the sanitized DB still provide accurate responses to queries. The central contribution of this work is to characterize the amount of information preserved in an optimal DP DB sanitizing mechanism (DSM). We precisely characterize the utility-privacy trade-off of mechanisms that sanitize DBs in the asymptotic regime of large DBs. We study this in an information-theoretic framework by modeling a generic distribution on the data, and a measure of fidelity between the histograms of the original and sanitized DBs. We consider the popular $\mathbb{L}_{1}-$distortion metric that leads to the formulation as a linear program (LP). This optimization problem is prohibitive in complexity with the number of constraints growing exponentially in the parameters of the problem. Leveraging tools from discrete geometry, analytic combinatorics, and duality theorems of optimization, we fully characterize the optimal solution in terms of a power series whose coefficients are the number of integer points on a multidimensional convex polytope studied by Ehrhart in 1967. Employing Ehrhart theory, we determine a simple closed form computable expression for the asymptotic growth of the optimal privacy-fidelity trade-off to infinite precision. At the heart of the findings is a deep connection between the minimum expected distortion and the Ehrhart series of an integral convex polytope.

cs.IT↗

arXiv2017

Communicating Correlated Sources Over an Interference Channel

A new coding technique, based on \textit{fixed block-length} codes, is proposed for the problem of communicating a pair of correlated sources over a $2-$user interference channel. Its performance is analyzed to derive a new set of sufficient conditions. The latter is proven to be strictly less binding than the current known best, which is due to Liu and Chen [Dec, 2011]. Our findings are inspired by Dueck's example [March, 1981].

cs.IT↗

arXiv2015

Coset codes for communicating over non-additive channels

We present a case for the use of codes possessing algebraic closure properties - coset codes - in developing coding techniques and characterizing achievable rate regions for generic multi-terminal channels. In particular, we consider three diverse communication scenarios - $3-$user interference channel (many-to-many), $3-$user broadcast channel (one-to-many), and multiple access with distributed states (many-to-one) - and identify non-additive examples for which coset codes are analytically proven to yield strictly larger achievable rate regions than those achievable using iid codes. On the one hand, our findings motivate the need for multi-terminal information theory to step beyond iid codes. On the other, it encourages current research of linear code-based techniques to go beyond particular additive communication channels. Detailed proofs of our results are available in [1]-[3].

cs.IT↗