Related papers: Generalized weights and bounds for error probabili…
We present novel bounds on the capacity of the independent and identically distributed binary deletion channel. Four upper bounds are obtained by providing the transmitter and the receiver with genie-aided information on suitably-defined…
We consider a generalization of the discrete memoryless channel, in which the channel probability distribution is replaced by a uniform distribution over clouds of channel output sequences. For a random ensemble of such channels, we derive…
An upper bound on the error probability of specific lattices, based on their distance-spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers.…
In this work, we introduce a generalization of the Landauer bound for erasure processes that stems from absolutely irreversible dynamics. Assuming that the erasure process is carried out in an absolutely irreversible way so that the…
We define generalized Hamming weights for almost affine codes. We show how various aspects and applications of generalized Hamming weights for linear codes, such as Wei duality, generalized Kung's bound, profiles, connection to wire-tap…
The problem of channel coding with the erasure option is revisited for discrete memoryless channels. The interplay between the code rate, the undetected and total error probabilities is characterized. Using the information spectrum method,…
In contrast to a maximum-likelihood decoder, it is often desirable to use an incomplete decoder that can detect its decoding errors with high probability. One common choice is the bounded distance decoder. Bounds are derived for the total…
We derive upper and lower bounds for the covert capacity of Additive White Gaussian Noise channels when measuring reliability in terms of the average error probability and covertness in terms of Kullback-Leibler divergence. This…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
In statistical learning theory, generalization error is used to quantify the degree to which a supervised machine learning algorithm may overfit to training data. Recent work [Xu and Raginsky (2017)] has established a bound on the…
A new lower bound for the average probability or error for a two-user discrete memoryless (DM) multiple-access channel (MAC) is derived. This bound has a structure very similar to the well-known sphere packing packing bound derived by…
We develop upper bounds on code size for an independent and identically distributed deletion and insertion channels for a given code length and target frame error probability. The bounds are obtained as a variation of a general converse…
We develop several lower bounds on the capacity of binary input symmetric output channels with synchronization errors which also suffer from other types of impairments such as substitutions, erasures, additive white Gaussian noise (AWGN)…
Generalization error bounds are critical to understanding the performance of machine learning models. In this work, building upon a new bound of the expected value of an arbitrary function of the population and empirical risk of a learning…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…
The generalized Hamming weights of a linear code have been extensively studied since Wei first use them to characterize the cryptography performance of a linear code over the wire-tap channel of type II. In this paper, we investigate the…
In this paper, parameterized Gallager's first bounding technique (GFBT) is presented by introducing nested Gallager regions, to derive upper bounds on the ML decoding error probability of general codes over AWGN channels. The three…
We establish a margin based data dependent generalization error bound for a general family of deep neural networks in terms of the depth and width, as well as the Jacobian of the networks. Through introducing a new characterization of the…
In parameter estimation, assumptions about the model are typically considered which allow us to build optimal estimation methods under many statistical senses. However, it is usually the case where such models are inaccurately known or not…
An information-theoretic upper bound on the generalization error of supervised learning algorithms is derived. The bound is constructed in terms of the mutual information between each individual training sample and the output of the…