Related papers: Decoding by Sampling: A Randomized Lattice Algorit…
The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders (ISD). However, recently…
The unadjusted Langevin algorithm is widely used for sampling from complex high-dimensional distributions. It is well known to be biased, with the bias typically scaling linearly with the dimension when measured in squared Wasserstein…
Approximate Bayesian Computation (ABC) is a popular sampling method in applications involving intractable likelihood functions. Without evaluating the likelihood function, ABC approximates the posterior distribution by the set of accepted…
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector…
This paper addresses the task of estimating a covariance matrix under a patternless sparsity assumption. In contrast to existing approaches based on thresholding or shrinkage penalties, we propose a likelihood-based method that regularizes…
Approximate Bayesian computation (ABC) methods are standard tools for inferring parameters of complex models when the likelihood function is analytically intractable. A popular approach to improving the poor acceptance rate of the basic…
As the number of samples and dimensionality of optimization problems related to statistics an machine learning explode, block coordinate descent algorithms have gained popularity since they reduce the original problem to several smaller…
In this paper, we present a low-diameter decomposition algorithm in the LOCAL model of distributed computing that succeeds with probability $1 - 1/poly(n)$. Specifically, we show how to compute an $\left(\epsilon, O\left(\frac{\log…
In this work, we propose a first-order sampling method called the Metropolis-adjusted Preconditioned Langevin Algorithm for approximate sampling from a target distribution whose support is a proper convex subset of $\mathbb{R}^{d}$. Our…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
This paper proposes a parallel computation strategy and a posterior-based lattice expansion algorithm for efficient lattice rescoring with neural language models (LMs) for automatic speech recognition. First, lattices from first-pass…
We present a construction of subspace codes along with an efficient algorithm for list decoding from both insertions and deletions, handling an information-theoretically maximum fraction of these with polynomially small rate. Our…
In this paper we present a minimal list decoding algorithm for Reed-Solomon (RS) codes. Minimal list decoding for a code $C$ refers to list decoding with radius $L$, where $L$ is the minimum of the distances between the received word…
The recent development of deep learning methods provides a new approach to optimize the belief propagation (BP) decoding of linear codes. However, the limitation of existing works is that the scale of neural networks increases rapidly with…
Linear programming (LP) decoding approximates maximum-likelihood (ML) decoding of a linear block code by relaxing the equivalent ML integer programming (IP) problem into a more easily solved LP problem. The LP problem is defined by a set of…
We address the problem of recovering a sparse signal from clipped or quantized measurements. We show how these two problems can be formulated as minimizing the distance to a convex feasibility set, which provides a convex and differentiable…
Spatial coupling is utilized to improve the performance of iterative channel estimation, multiuser detection, and decoding for multiple-input multiple-input (MIMO) bit-interleaved coded modulation (BICM). Coupling is applied to both coding…
Weighted least squares polynomial approximation uses random samples to determine projections of functions onto spaces of polynomials. It has been shown that, using an optimal distribution of sample locations, the number of samples required…
Spinal codes are a type of capacity-achieving rateless codes that have been proved to approach the Shannon capacity over the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC). In this paper, we aim to…
Since the classical work of Berlekamp, McEliece and van Tilborg, it is well known that the problem of exact maximum-likelihood (ML) decoding of general linear codes is NP-hard. In this paper, we show that exact ML decoding of a classs of…