Related papers: Achievable Rates for Probabilistic Shaping
It is well known that a random q-ary code of rate \Omega(\epsilon^2) is list decodable up to radius (1 - 1/q - \epsilon) with list sizes on the order of 1/\epsilon^2, with probability 1 - o(1). However, until recently, a similar statement…
Rejection sampling is a technique for sampling from difficult distributions. However, its use is limited due to a high rejection rate. Common adaptive rejection sampling methods either work only for very specific distributions or without…
We study maximum likelihood estimation for spatial generalized linear mixed models with Gaussian process approximations using a stochastic Newton-Raphson algorithm. We consider two Gaussian Process approximations in this context: spectral…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
Sparse random linear network coding (SRLNC) used as a class of erasure codes to ensure the reliability of multicast communications has been widely investigated. However, an exact expression for the decoding success probability of SRLNC is…
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
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…
In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn…
Convolutional precoding in polarization-adjusted convolutional (PAC) codes can reduce the number of minimum weight codewords (a.k.a error coefficient) of polar codes. This can result in improving the error correction performance of (near)…
Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by…
We derive computable error estimates for finite element approximations of linear elliptic partial differential equations (PDE) with rough stochastic coefficients. In this setting, the exact solutions contain high frequency content that…
Estimating probabilistic deformable template models is a new approach in the fields of computer vision and probabilistic atlases in computational anatomy. A first coherent statistical framework modelling the variability as a hidden random…
The problem of error correction for Gallager's low-density parity-check codes is famously equivalent to that of computing marginal Boltzmann probabilities for an Ising-like model with multispin interactions in a non-uniform magnetic field.…
A new polar coding scheme for higher order modulation is presented. The proposed scheme is based on multi-level coding (MLC) with natural labeling, where the bit-level corresponding to the sign-bit is generated in dependence on the previous…
Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides…
This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
We propose and study a task we name panoptic segmentation (PS). Panoptic segmentation unifies the typically distinct tasks of semantic segmentation (assign a class label to each pixel) and instance segmentation (detect and segment each…
Decoders built on Gaussian processes (GPs) are enticing due to the marginalisation over the non-linear function space. Such models (also known as GP-LVMs) are often expensive and notoriously difficult to train in practice, but can be scaled…
We propose a new partial decoding algorithm for $m$-interleaved Reed--Solomon (IRS) codes that can decode, with high probability, a random error of relative weight $1-R^{\frac{m}{m+1}}$ at all code rates $R$, in time polynomial in the code…
A probabilistic approach of computing geometric rate of convergence of stochastic processes is introduced in this paper. The goal is to quantitatively compute both upper and lower bounds of the exponential rate of convergence to the…