Related papers: Generalized weights and bounds for error probabili…
Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and…
Upper bounds on the maximum number of codewords in a binary code of a given length and minimum Hamming distance are considered. New bounds are derived by a combination of linear programming and counting arguments. Some of these bounds…
An alternative to extrinsic information transfer (EXIT) charts called mean squared error (MSE) charts that use a measure related to the MSE instead of mutual information is proposed. Using the relationship between mutual information and…
This paper is concerned with the channel estimation problem in millimetre wave (MMW) wireless systems with large antenna arrays. By exploiting the sparse nature of the MMW channel, we present an efficient estimation algorithm based on a…
It has been experimentally observed in recent years that multi-layer artificial neural networks have a surprising ability to generalize, even when trained with far more parameters than observations. Is there a theoretical basis for this?…
Reducible codes for the rank metric were introduced for cryptographic purposes. They have fast encoding and decoding algorithms, include maximum rank distance (MRD) codes and can correct many rank errors beyond half of their minimum rank…
Mixed-dimensional elliptic equations exhibiting a hierarchical structure are commonly used to model problems with high aspect ratio inclusions, such as flow in fractured porous media. We derive general abstract estimates based on the theory…
Deep neural networks (DNNs) exhibit an exceptional capacity for generalization in practical applications. This work aims to capture the effect and benefits of depth for supervised learning via information-theoretic generalization bounds. We…
Current PAC-Bayes generalisation bounds are restricted to scalar metrics of performance, such as the loss or error rate. However, one ideally wants more information-rich certificates that control the entire distribution of possible…
There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises,…
By exploiting a generalization of recent results on environment-assisted channel correction, we show that, whenever a quantum system undergoes a channel realized as an interaction with a probe, the more efficiently the information about the…
Generalization is a central concept in machine learning theory, yet for quantum models, it is predominantly analyzed through uniform bounds that depend on a model's overall capacity rather than the specific function learned. These…
At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data. While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our…
Through refined asymptotic analysis based on the normal approximation, we study how higher-order coding performance depends on the mean power as well as on finer statistics of the input power. We introduce a multifaceted power model in…
This paper provides a general technique for lower bounding the Bayes risk of statistical estimation, applicable to arbitrary loss functions and arbitrary prior distributions. A lower bound on the Bayes risk not only serves as a lower bound…
We consider information-theoretic bounds on expected generalization error for statistical learning problems in a networked setting. In this setting, there are $K$ nodes, each with its own independent dataset, and the models from each node…
New channel coding converse and achievability bounds are derived for a single use of an arbitrary channel. Both bounds are expressed using a quantity called the "smooth 0-divergence", which is a generalization of Renyi's divergence of order…
We derive a sphere-packing error exponent for coded transmission over discrete memoryless channels with a fixed decoding metric. By studying the error probability of the code over an auxiliary channel, we find a lower bound to the…
In this paper, we investigate the optimal tradeoff between source and channel coding for channels with bit or packet erasure. Upper and Lower bounds on the optimal channel coding rate are computed to achieve minimal end-to-end distortion.…
In this article, we consider scenarios in which traditional estimates for the active subspace method based on probabilistic Poincar\'e inequalities are not valid due to unbounded Poincar\'e constants. Consequently, we propose a framework…