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In this paper, we derive Gallager's random coding error exponent for multiple-input multiple-output (MIMO) channels, assuming no channel-state information (CSI) at the transmitter and perfect CSI at the receiver. This measure gives insight…

Information Theory · Computer Science 2007-07-13 Hyundong Shin , Moe Z. Win

Csisz\'ar's channel coding theorem for multiple codebooks is generalized allowing the codeword lenghts differ across codebooks. Also in this case, for each codebook an error exponent can be achieved that equals the random coding exponent…

Information Theory · Computer Science 2017-01-24 Lóránt Farkas , Tamás Kói

This paper introduces a novel error estimator for the Proper Generalized Decomposition (PGD) approximation of parametrized equations. The estimator is intrinsically random: It builds on concentration inequalities of Gaussian maps and an…

Numerical Analysis · Mathematics 2019-10-28 Kathrin Smetana , Olivier Zahm

We analyze the sample complexity of full-batch Gradient Descent (GD) in the setup of non-smooth Stochastic Convex Optimization. We show that the generalization error of GD, with common choice of hyper-parameters, can be $\tilde \Theta(d/m +…

Machine Learning · Computer Science 2024-04-12 Roi Livni

We provide two results concerning the optimality of the maximum mutual information (MMI) decoder. First, we prove that the error exponents of the typical random codes under the optimal maximum likelihood (ML) decoder and the MMI decoder are…

Information Theory · Computer Science 2020-07-27 Ran Tamir , Neri Merhav

We consider the probability that a weighted sum of $n$ i.i.d. random variables $X_j$, $j = 1, . . ., n$, with stretched exponential tails is larger than its expectation and determine the rate of its decay, under suitable conditions on the…

Probability · Mathematics 2014-12-30 Nina Gantert , Kavita Ramanan , Franz Rembart

This work contains two main contributions concerning the expurgation of hierarchical ensembles for the asymmetric broadcast channel. The first is an analysis of the optimal maximum likelihood (ML) decoders for the weak and strong user. Two…

Information Theory · Computer Science 2017-11-29 Ran Averbuch , Nir Weinberger , Neri Merhav

We study the problem of universal decoding for unknown discrete memoryless channels in the presence of erasure/list option at the decoder, in the random coding regime. Specifically, we harness a universal version of Forney's classical…

Information Theory · Computer Science 2017-06-23 Wasim Huleihel , Nir Weinberger , Neri Merhav

Some new results are derived concerning random coding error exponents and expurgated exponents for list decoding with a deterministic list size $L$. Two asymptotic regimes are considered, the fixed list-size regime, where $L$ is fixed…

Information Theory · Computer Science 2016-11-17 Neri Merhav

In this paper, we study error exponents for a concatataned coding based class of DNA storage codes in which the number of reads performed can be variable. That is, the decoder can sequentially perform reads and choose whether to output the…

Information Theory · Computer Science 2025-04-25 Yan Hao Ling , Nir Weinberger , Jonathan Scarlett

The security level of the achievability scheme for Wyner's wiretap channel model is examined from the perspective of the probability of correct decoding, $P_c$, at the wiretap channel decoder. In particular, for finite-alphabet memoryless…

Information Theory · Computer Science 2016-11-17 Neri Merhav

The error exponent of fixed-length lossy source coding was established by Marton. Ahlswede showed that this exponent can be discontinuous at a rate $R$, depending on the probability distribution $P$ of the given information source and the…

Information Theory · Computer Science 2023-04-25 Yutaka Jitsumatsu

We establish maximal concentration bounds for the iterates generated by stochastic approximation algorithms with general step sizes, where the noise has a finite-state Markovian component plus a Martingale-difference component. When the…

Probability · Mathematics 2026-05-21 Shubhada Agrawal , Siva Theja Maguluri , Martin Zubeldia

In this paper, we prove that the sub-field images of generalized Reed-Solomon (RS) codes can achieve the symmetric capacity of p-ary memoryless channels. Unlike the totally random linear code ensemble, as a class of maximum distance…

Information Theory · Computer Science 2025-05-14 Xiangping Zheng , Xiao Ma

The problem of learning tree-structured Gaussian graphical models from independent and identically distributed (i.i.d.) samples is considered. The influence of the tree structure and the parameters of the Gaussian distribution on the…

Machine Learning · Statistics 2010-05-06 Vincent Y. F. Tan , Animashree Anandkumar , Alan S. Willsky

Generalized product codes (GPCs) are extensions of product codes (PCs) where code symbols are protected by two component codes but not necessarily arranged in a rectangular array. We consider a deterministic construction of GPCs (as opposed…

Information Theory · Computer Science 2017-02-28 Christian Häger , Henry D. Pfister , Alexandre Graell i Amat , Fredrik Brännström

We derive upper and lower bounds for the error exponents of lossless streaming compression of two correlated sources under the blockwise and symbolwise settings. We consider the linear scaling regime in which the delay is a scalar multiple…

Information Theory · Computer Science 2016-02-24 Lin Zhou , Vincent Yan Fu Tan , Mehul Motani

A lower bound on the maximum likelihood (ML) decoding error exponent of linear block code ensembles, on the erasure channel, is developed. The lower bound turns to be positive, over an ensemble specific interval of erasure probabilities,…

Information Theory · Computer Science 2019-01-23 Enrico Paolini , Gianluigi Liva

We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…

Information Theory · Computer Science 2024-09-10 Masahito Hayashi

We address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel. An improved upper bound is given for the maximum…

Information Theory · Computer Science 2007-07-16 Alexander Barg , Andrew McGregor