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Large alphabets: Finite, infinite, and scaling models

Mesrob I. Ohannessian, Munther A. Dahleh
2012 2012 46th Annual Conference on Information Sciences and Systems (CISS)  
More generally, this gives rise to scaling models that strive to capture regimes of operation where one anticipates such imbalance. Large alphabets may also be idealized as infinite.  ...  In this paper we present an overview of models for large alphabets, some recent results, and possible directions in this area.  ...  SCALING MODELS Finite models for large alphabets, such as the ones we presented, and which are described as uniform consistency over classes of finite sources are adequate for directly capturing alphabet  ... 
doi:10.1109/ciss.2012.6310941 dblp:conf/ciss/OhannessianD12 fatcat:gwhz7ahgrfhxlecdbl5nefoo3u

Compressing Multisets with Large Alphabets [article]

Daniel Severo, James Townsend, Ashish Khisti, Alireza Makhzani, Karen Ullrich
2021 arXiv   pre-print
Current methods that optimally compress multisets are not suitable for high-dimensional symbols, as their compute time scales linearly with alphabet size.  ...  We present a method that can recover those bits, assuming symbols are i.i.d., at the cost of an additional 𝒪(|ℳ|log M) in average time complexity, where |ℳ| and M are the total and unique number of symbols  ...  In preparing this research, authors affiliated to the Vector Institute were funded, in part, by the Province of Ontario, the Government of Canada through CIFAR, and companies sponsoring the Vector Institute  ... 
arXiv:2107.09202v1 fatcat:xpmxlyp2nfbkllsnrhcnbdvupa

Spatially encoded light for Large-alphabet Quantum Key Distribution [article]

T.B.H. Tentrup, W.M. Luiten, R. van der Meer, P. Hooijschuur, and P.W.H. Pinkse
2019 arXiv   pre-print
Employing this higher-dimensional Hilbert space together with modern single-photon-detecting cameras, we demonstrate a proof-of-principle large-alphabet Quantum Key Distribution experiment with 1024 symbols  ...  and a shared information between sender and receiver of 7 bit per photon.  ...  Due to the finite key length the error correction has a finite failure probability and not all errors can be removed.  ... 
arXiv:1808.02823v3 fatcat:f6v2s3mqs5h75cy4rol727tli4

Minimax rates of entropy estimation on large alphabets via best polynomial approximation [article]

Yihong Wu, Pengkun Yang
2016 arXiv   pre-print
This refines the recent result of Valiant-Valiant VV11 that the minimal sample size for consistent entropy estimation scales according to Θ(k/ k).  ...  The apparatus of best polynomial approximation plays a key role in both the construction of optimal estimators and, via a duality argument, the minimax lower bound.  ...  However, the convergence rate of the bias can be arbitrarily slow on a possibly infinite alphabet.  ... 
arXiv:1407.0381v3 fatcat:jmbcjthr4zdrfnyqvdfd757tte

Coding for the Large-Alphabet Adversarial Channel

Ebad Ahmed, Aaron B. Wagner
2017 IEEE Transactions on Information Theory  
For this fixed-blocklength, "large alphabet" channel, we show that combining an optimal rate-distortion code with an optimal error-correction code yields an optimal overall code for Gaussian sources with  ...  quadratic distortion and binary uniform sources with Hamming distortion but that it can be suboptimal by an arbitrarily-large factor in general.  ...  and especially for calling attention to the work of Dolev et al  ... 
doi:10.1109/tit.2017.2725280 fatcat:7vfwbqmba5fdvfxfjftqihrwdi

Classification of Homogeneous Data With Large Alphabets

Benjamin G. Kelly, Aaron B. Wagner, Thitidej Tularak, Pramod Viswanath
2013 IEEE Transactions on Information Theory  
To better model sources such as natural language, for which the underlying distributions are difficult to learn, we allow the alphabet size to grow and therefore the probability distributions to change  ...  Our primary focus is the situation in which the underlying probabilities are all of the same order, and in this regime we give conditions on the alphabet growth rate and distributions guaranteeing the  ...  Yet, for α-large alphabet sources these differences are naturally on the same scale and we show that this normalization can cause a systematic inconsistency.  ... 
doi:10.1109/tit.2012.2222343 fatcat:ntueclppvfcsjgoeqonmrqlm44

Sequential Probability Assignment with Binary Alphabets and Large Classes of Experts [article]

Alexander Rakhlin, Karthik Sridharan
2015 arXiv   pre-print
We analyze the problem of sequential probability assignment for binary outcomes with side information and logarithmic loss, where regret---or, redundancy---is measured with respect to a (possibly infinite  ...  We also consider an example of a large class of experts parametrized by vectors in a high-dimensional Euclidean ball (or a Hilbert ball).  ...  Acknowledgements We gratefully acknowledge the support of NSF under grants CAREER DMS-0954737 and CCF-1116928, as well as Dean's Research Fund.  ... 
arXiv:1501.07340v1 fatcat:cesbyxi54je4vbktrsx6pizdlm

Large Alphabet Compression and Predictive Distributions through Poissonization and Tilting [article]

Xiao Yang, Andrew R. Barron
2014 arXiv   pre-print
This paper introduces a convenient strategy for coding and predicting sequences of independent, identically distributed random variables generated from a large alphabet of size m.  ...  The employment of a Poisson model and tilting method simplifies the implementation and analysis through independence.  ...  Mokshay Madiman and Prof. Joseph Chang for their helpful advice and consistent support. They are also grateful to the family-like department and classmates, which makes all of these possible.  ... 
arXiv:1401.3760v1 fatcat:t726cqjd7fbkpeme2mjassn2pe

Large-alphabet encoding for higher-rate quantum key distribution

Catherine Lee, Darius Bunandar, Zheshen Zhang, Gregory R. Steinbrecher, P. Ben Dixon, Franco N. C. Wong, Jeffrey H. Shapiro, Scott A. Hamilton, Dirk Englund
2019 Optics Express  
High-dimensional encoding is possible in a variety of degrees of freedom, and large-alphabet  ...  Compared to binary-encoded QKD, such large-alphabet schemes can boost secure communication rates by encoding more secure information per detected photon and also exhibit increased resilience to noise and  ...  count rate were modeled following [37] .  ... 
doi:10.1364/oe.27.017539 fatcat:4wuaepeylvhwbctx74kt27yqvu

Minimax Pointwise Redundancy for Memoryless Models Over Large Alphabets

Wojciech Szpankowski, Marcelo J. Weinberger
2012 IEEE Transactions on Information Theory  
We study the minimax pointwise redundancy of universal coding for memoryless models over large alphabets and present two main results: We first complete studies initiated in Orlitsky and Santhanam [15]  ...  Our findings can be used to approximate numerically the minimax pointwise redundancy for various ranges of the sequence length and the alphabet size.  ...  Specifically, we consider the alphabet A ∪ B, with |A| = m and |B| = M , and a (memoryless) model family, denoted M 0 , in which the probabilities of symbols in B are fixed, while m may be large. 2 Such  ... 
doi:10.1109/tit.2012.2195769 fatcat:fxomy5kz6jghlaa5nkkillfgpe

Compression and predictive distributions for large alphabet i.i.d and Markov models

Xiao Yang, Andrew R. Barron
2014 2014 IEEE International Symposium on Information Theory  
This paper considers coding and predicting sequences of random variables generated from a large alphabet.  ...  We start from the i.i.d model and propose a simple coding distribution formulated by a product of tilted Poisson distributions which achieves close to optimal performance.  ...  Wojciech Szpankowski and Prof. Narayana Santhanam.  ... 
doi:10.1109/isit.2014.6875285 dblp:conf/isit/YangB14 fatcat:e7axpnquyjcodft2lgcsxx6knu

On redundancy of memoryless sources over countable alphabets [article]

Maryam Hosseini, Narayana Santhanam
2014 arXiv   pre-print
This formulation is fundamental to problems not just in compression, but also estimation and prediction and has a wide variety of applications from language modeling to insurance.  ...  We first show that if describing a single sample from P incurs finite redundancy, then P is tight but that the converse does not always hold.  ...  If the alphabet has size k, the redundancy of P is easily seen to be always finite (in fact ≤ log k) and that of P n scales as k 2 log n.  ... 
arXiv:1404.0062v1 fatcat:zuapfcz2hffvrl77murys3zkum

On Finite Alphabet Compressive Sensing [article]

Abhik Kumar Das, Sriram Vishwanath
2013 arXiv   pre-print
We show that there are significant benefits to analyzing the problem while incorporating its finite alphabet nature, versus ignoring it and employing a conventional real alphabet based toolbox.  ...  This paper considers the problem of compressive sensing over a finite alphabet, where the finite alphabet may be inherent to the nature of the data or a result of quantization.  ...  use of linear codes over finite fields of large sizes.  ... 
arXiv:1303.3943v1 fatcat:obmxdfmzkbaspozmzrukq7oyje

Discovering a domain alphabet

Michael D. Schmidt, Hod Lipson
2009 Proceedings of the 11th Annual conference on Genetic and evolutionary computation - GECCO '09  
An alphabet that is too granular may generate an unnecessarily large search space; an inappropriately coarse grained alphabet may bias or prevent finding optimal solutions.  ...  We suggest that identifying a problem-specific alphabet is key to scaling evolutionary methods to higher complexity systems.  ...  National Science Foundation Graduate Research Fellowship Program, and U.S. National Science Foundation Grant CMMI 0547376.  ... 
doi:10.1145/1569901.1570047 dblp:conf/gecco/SchmidtL09 fatcat:l5gnoep4rnh2dp3wmu5g2brkwy

Joint Semi-blind Channel Estimation and Finite Alphabet Signal Recovery Detection for large-scale MIMO systems

Zahran Hajji, Abdeldjalil Aissa-El-Bey, Karine Amis
2021 IEEE Open Journal of Signal Processing  
In this paper, we consider large-scale MIMO systems and we address the channel estimation problem.  ...  We propose an iterative receiver consisting of the cascade of a semi-blind leastsquares channel estimation algorithm with a simplicity-based detection algorithm for finite-alphabet signals (FAS and FAS-SAC  ...  When N and n take high values, the resulting model amounts to a large-scale MIMO system with N inputs and n outputs.  ... 
doi:10.1109/ojsp.2021.3097968 fatcat:6s4rq54wxzbbphfmykkxvuoaom
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