arXiv subjects

S. Sandeep Pradhan

Publications and source records attributed to S. Sandeep Pradhan.

At least 37 records · Page 2Linked to original sources

arXiv2022

Lattices from Linear Codes: Source and Channel Networks

In this paper, we consider the information-theoretic characterization of the set of achievable rates and distortions in a broad class of multiterminal communication scenarios with general continuous-valued sources and channels. A framework is presented which involves fine discretization of the source and channel variables followed by communication over the resulting discretized network. In order to evaluate fundamental performance limits, convergence results for information measures are provided under the proposed discretization process. Using this framework, we consider point-to-point source coding and channel coding with side-information, distributed source coding with distortion constraints, the function reconstruction problems (two-help-one), computation over multiple access channel, the interference channel, and the multiple-descriptions source coding problem. We construct lattice-like codes for general sources and channels, and derive inner-bounds to set of achievable rates and distortions in these communication scenarios.

cs.IT↗

arXiv2022

Upper Bounds on the Feedback Error Exponent of Channels With States and Memory

As a class of state-dependent channels, Markov channels have been long studied in information theory for characterizing the feedback capacity and error exponent. This paper studies a more general variant of such channels where the state evolves via a general stochastic process, not necessarily Markov or ergodic. The states are assumed to be unknown to the transmitter and the receiver, but the underlying probability distributions are known. For this setup, we derive an upper bound on the feedback error exponent and the feedback capacity with variable-length codes. The bounds are expressed in terms of the directed mutual information and directed relative entropy. The bounds on the error exponent are simplified to Burnashev's expression for discrete memoryless channels. Our method relies on tools from the theory of martingales to analyze a stochastic process defined based on the entropy of the message given the past channel's outputs.

cs.IT↗

arXiv2021

Distributed Quantum Faithful Simulation and Function Computation Using Algebraic Structured Measurements

In this work, we consider the task of faithfully simulating a quantum measurement, acting on a joint bipartite quantum state, in a distributed manner. In the distributed setup, the constituent sub-systems of the joint quantum state are measured by two agents, Alice and Bob. A third agent, Charlie receives the measurement outcomes sent by Alice and Bob. Charlie uses local and pairwise shared randomness to compute a bivariate function of the measurement outcomes. The objective of three agents is to faithfully simulate the given distributed quantum measurement acting on the given quantum state while minimizing the communication and shared randomness rates. We demonstrate a new achievable information-theoretic rate-region that exploits the bivariate function using random structured POVMs based on asymptotically good algebraic codes. The algebraic structure of these codes is matched to that of the bivariate function that models the action of Charlie. The conventional approach for this class of problems has been to reconstruct individual measurement outcomes corresponding to Alice and Bob, at Charlie, and then compute the bivariate function, achieved using mutually independent approximating POVMs based on random unstructured codes. In the present approach, using algebraic structured POVMs, the computation is performed on the fly, thus obviating the need to reconstruct individual measurement outcomes at Charlie. Using this, we show that a strictly larger rate region can be achieved. One of the challenges in analyzing these structured POVMs is that they exhibit only pairwise independence and induce only uniform single-letter distributions. To address this, we use nesting of algebraic codes and develop a covering lemma applicable to pairwise-independent POVM ensembles. Combining these techniques, we provide a multi-party distributed faithful simulation and function computation protocol.

cs.IT↗

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↗

arXiv2020

A New Achievable Rate-Distortion Region for Distributed Source Coding

In this work, lossy distributed compression of pairs of correlated sources is considered. Conventionally, Shannon's random coding arguments -- using randomly generated unstructured codebooks whose blocklength is taken to be asymptotically large -- are used to derive achievability results. However, it was recently observed that in various multi-terminal communications scenarios, using random codes with constant finite blocklength may lead to improved achievable regions compared to the conventional approach. In other words, in some network communication scenarios, there is a finite optimal value in the blocklength of the randomly generated code used for distributed processing of information sources. Motivated by this, a coding scheme is proposed which consists of two codebook layers: i) the primary codebook which has constant finite blocklength, and ii) the secondary codebook whose blocklength is taken to be asymptotically large. The achievable region is analyzed in two steps. In the first step, a characterization of the achievable region is derived using information measures which are functions of multi-letter probability distributions. In the next step, a computable single-letter inner-bound to the achievable region is derived. It is shown through several examples that the resulting rate-distortion region is strictly larger than the Berger Tung achievable region.

cs.IT↗

arXiv2020

Faithful Simulation of Distributed Quantum Measurements with Applications in Distributed Rate-Distortion Theory

We consider the task of faithfully simulating a distributed quantum measurement, wherein we provide a protocol for the three parties, Alice, Bob and Eve, to simulate a repeated action of a distributed quantum measurement using a pair of non-product approximating measurements by Alice and Bob, followed by a stochastic mapping at Eve. The objective of the protocol is to utilize minimum resources, in terms of classical bits needed by Alice and Bob to communicate their measurement outcomes to Eve, and the common randomness shared among the three parties, while faithfully simulating independent repeated instances of the original measurement. To achieve this, we develop a mutual covering lemma and a technique for random binning of distributed quantum measurements, and, in turn, characterize a set of sufficient communication and common randomness rates required for asymptotic simulatability in terms of single-letter quantum information quantities. Furthermore, using these results we address a distributed quantum rate-distortion problem, where we characterize the achievable rate-distortion region through a single-letter inner bound. Finally, via a technique of single-letterization of multi-letter quantum information quantities, we provide an outer bound for the rate-distortion region.

cs.IT↗

arXiv2020

Coding for Crowdsourced Classification with XOR Queries

This paper models the crowdsourced labeling/classification problem as a sparsely encoded source coding problem, where each query answer, regarded as a code bit, is the XOR of a small number of labels, as source information bits. In this paper we leverage the connections between this problem and well-studied codes with sparse representations for the channel coding problem to provide querying schemes with almost optimal number of queries, each of which involving only a constant number of labels. We also extend this scenario to the case where some workers can be unresponsive. For this case, we propose querying schemes where each query involves only log n items, where n is the total number of items to be labeled. Furthermore, we consider classification of two correlated labeling systems and provide two-stage querying schemes with almost optimal number of queries each involving a constant number of labels.

stat.ML↗

arXiv2020

Capacity-achieving Polar-based LDGM Codes with Crowdsourcing Applications

In this paper we study codes with sparse generator matrices. More specifically, codes with a certain constraint on the weight of all the columns in the generator matrix are considered. The end result is the following. For any binary-input memoryless symmetric (BMS) channel and any epsilon > 2 epsilon*, where epsilon^* = \frac{1}{6}-\frac{5}{3}\log{\frac{4}{3}} \approx 0.085, we show an explicit sequence of capacity-achieving codes with all the column wights of the generator matrix upper bounded by (\log N)^{1+epsilon}, where N is the code block length. The constructions are based on polar codes. Applications to crowdsourcing are also shown.

eess.SP↗

arXiv2019

Supertranslation Hair of Schwarzschild Black Hole: A Wilson Line Perspective

We demonstrate within the quantum field theoretical framework that an asymptotic particle falling into the black hole implants soft graviton hair on the horizon, conforming with the classical proposal of Hawking, Perry and Strominger. A key ingredient to this result is the construction of gravitational Wilson line dressings of an infalling scalar field, carrying a definite horizon supertranslation charge. It is shown that a typical Schwarzschild state is degenerate, and can be labeled by different soft supertranslation hairs parametrized for radial trajectories by the mass and energy of the infalling particle and its asymptotic point of contact with the horizon. The supertranslation zero modes are also obtained in terms of zero-frequency graviton operators, and are shown to be the expected canonical partners of the linearized horizon charge that enlarge the horizon Hilbert space.

hep-th↗

arXiv2019

Boolean Functions with Biased Inputs: Approximation and Noise Sensitivity

This paper considers the problem of approximating a Boolean function $f$ using another Boolean function from a specified class. Two classes of approximating functions are considered: $k$-juntas, and linear Boolean functions. The $n$ input bits of the function are assumed to be independently drawn from a distribution that may be biased. The quality of approximation is measured by the mismatch probability between $f$ and the approximating function $g$. For each class, the optimal approximation and the associated mismatch probability is characterized in terms of the biased Fourier expansion of $f$. The technique used to analyze the mismatch probability also yields an expression for the noise sensitivity of $f$ in terms of the biased Fourier coefficients, under a general i.i.d. input perturbation model.

cs.IT↗

arXiv2019

Structured Mappings and Conferencing Common Information for Multiple-access Channels

In this work, we study two problems: three-user Multiple-Access Channel (MAC) with correlated sources, and MAC with Feedback (MAC-FB) with independent messages. For the first problem, we identify a structure in the joint probability distribution of discrete memoryless sources, and define a new common information called ``conferencing common information". We develop a multi-user joint-source channel coding methodology based on structured mappings to encode this common information efficiently and to transmit it over a MAC. We derive a new set of sufficient conditions for this coding strategy using single-letter information quantities for arbitrary sources and channel distributions. Next, we make a fundamental connection between this problem and the problem of communication of independent messages over three-user MAC-FB. In the latter problem, although the messages are independent to begin with, they become progressively correlated given the channel output feedback. Subsequent communication can be modeled as transmission of correlated sources over MAC. Exploiting this connection, we develop a new coding scheme for the problem. We characterize its performance using single-letter information quantities, and derive an inner bound to the capacity region. For both problems, we provide a set of examples where these rate regions are shown to be optimal. Moreover, we analytically prove that this performance is not achievable using random unstructured random mappings/codes.

cs.IT↗

arXiv2018

On The Reliability Function of Discrete Memoryless Multiple-Access Channel with Feedback

We derive a lower and upper bound on the reliability function of discrete memoryless multiple-access channel (MAC) with noiseless feedback and variable-length codes (VLCs). For the upper-bound, we use proof techniques of Burnashev for the point-to-point case. Also, we adopt the techniques used to prove the converse for the feedback-capacity of MAC. For the lower-bound on the error exponent, we present a coding scheme consisting of a data and a confirmation stage. In the data stage, any arbitrary feedback capacity-achieving code is used. In the confirmation stage, each transmitter sends one bit of information to the receiver using a pair of codebooks of size two, one for each transmitter. The codewords at this stage are selected randomly according to an appropriately optimized joint probability distribution. The bounds increase linearly with respect to a specific Euclidean distance measure defined between the transmission rate pair and the capacity boundary. The lower and upper bounds match for a class of MACs.

cs.IT↗

arXiv2018

Bounds on the Effective-length of Optimal Codes for Interference Channel with Feedback

In this paper, we investigate the necessity of finite blocklength codes in distributed transmission of independent message sets over channels with feedback. Previously, it was shown that finite effective length codes are necessary in distributed transmission and compression of sources. We provide two examples of three user interference channels with feedback where codes with asymptotically large effective lengths are sub-optimal. As a result, we conclude that coded transmission using finite effective length codes is necessary to achieve optimality. We argue that the sub-optimal performance of large effective length codes is due to their inefficiency in preserving the correlation between the inputs to the distributed terminals in the communication system. This correlation is made available by the presence of feedback at the terminals and is used as a means for coordination between the terminals when using finite effective length coding strategies.

cs.IT↗

arXiv2017

On the Sub-optimality of Single-Letter Coding over Networks

In this paper, we establish a new bound tying together the effective length and the maximum correlation between the outputs of an arbitrary pair of Boolean functions which operate on two sequences of correlated random variables. We derive a new upper bound on the correlation between the outputs of these functions. The upper bound may find applications in problems in many areas which deal with common information. We build upon Witsenhausen's result on maximum correlation. The present upper bound takes into account the effective length of the Boolean functions in characterizing the correlation. We use the new bound to characterize the communication-cooperation tradeoff in multi-terminal communications. We investigate binary block-codes (BBC). A BBC is defined as a vector of Boolean functions. We consider an ensemble of BBCs which is randomly generated using single-letter distributions. We characterize the vector of dependency spectrums of these BBCs. We use this vector to bound the correlation between the outputs of two distributed BBCs. Finally, the upper bound is used to show that the large blocklength single-letter coding schemes studied in the literature are sub-optimal in various multi-terminal communication settings.

cs.IT↗

arXiv2017

On the Necessity of Structured Codes for Communications over MAC with Feedback

The problem of three-user multiple-access channel (MAC) with noiseless feedback is investigated. A new coding strategy is presented. The coding scheme builds upon the natural extension of the Cover-Leung (CL) scheme; and uses quasi-linear codes. A new single-letter achievable rate region is derived. The new achievable region strictly contains the CL region. This is shown through an example. In this example, the coding scheme achieves optimality in terms of transmission rates. It is shown that any optimality achieving scheme for this example must have a specific algebraic structure. Particularly, the codebooks must be closed under binary addition.

cs.IT↗