Related papers: On Approximation, Bounding & Exact Calculation of …
In the short block length regime, ensemble decoding schemes with their inherently parallel structure can improve error correction performance and reduce latency compared to stand-alone suboptimal decoders such as belief propagation (BP). In…
A new efficient ensemble prediction strategy is developed for a general turbulent model framework with emphasis on the nonlinear interactions between large and small scale variables. The high computational cost in running large ensemble…
Given a probability distribution $\mathcal{D}$ over the non-negative integers, a $\mathcal{D}$-repeat channel acts on an input symbol by repeating it a number of times distributed as $\mathcal{D}$. For example, the binary deletion channel…
We show that the probability distribution of the error exponent in i.i.d. code ensembles over classical-quantum (CQ) channels with arbitrary output states accumulates above a threshold that is strictly larger than the CQ random coding…
Variable-length block-coding schemes are investigated for discrete memoryless channels with ideal feedback under cost constraints. Upper and lower bounds are found for the minimum achievable probability of decoding error $P_{e,\min}$ as a…
The likelihood decoder is a stochastic decoder that selects the decoded message at random, using the posterior distribution of the true underlying message given the channel output. In this work, we study a generalized version of this…
High-order clustering aims to identify heterogeneous substructures in multiway datasets that arise commonly in neuroimaging, genomics, social network studies, etc. The non-convex and discontinuous nature of this problem pose significant…
We propose a scalable algorithmic framework for exact Bayesian variable selection and model averaging in linear models under the assumption that the Gram matrix is block-diagonal, and as a heuristic for exploring the model space for general…
For the additive white Gaussian noise channel with average codeword power constraint, sparse superposition codes are developed. These codes are based on the statistical high-dimensional regression framework. The paper [IEEE Trans. Inform.…
Efficient and accurate decoding of quantum error-correcting codes is essential for fault-tolerant quantum computation, however, it is challenging due to the degeneracy of errors, the complex code topology, and the large space for logical…
We explain an algorithm that approximately but efficiently assesses particular parity-check error-correcting codes of large, but finite, blocklength. This algorithm is based on the ``renormalization-group'' approach from physics: the idea…
Channel simulation algorithms can efficiently encode random samples from a prescribed target distribution $Q$ and find applications in machine learning-based lossy data compression. However, algorithms that encode exact samples usually have…
To facilitate the numerical analysis of particle methods, we derive truncation error estimates for the approximate operators in a generalized particle method. Here, a generalized particle method is defined as a meshfree numerical method…
I will show that there is a deep relation between error-correction codes and certain mathematical models of spin glasses. In particular minimum error probability decoding is equivalent to finding the ground state of the corresponding spin…
We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions.…
Consider the following unequal error protection scenario. One special message, dubbed the "red alert" message, is required to have an extremely small probability of missed detection. The remainder of the messages must keep their average…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Many of the classic problems of coding theory are highly symmetric, which makes it easy to derive sphere-packing upper bounds and sphere-covering lower bounds on the size of codes. We discuss the generalizations of sphere-packing and…
This paper considers error probabilities of random codes for memoryless channels in the fixed-rate regime. Random coding is a fundamental scheme to achieve the channel capacity and many studies have been conducted for the asymptotics of the…
The error probability of block codes sent under a non-uniform input distribution over the memoryless binary symmetric channel (BSC) and decoded via the maximum a posteriori (MAP) decoding rule is investigated. It is proved that the ratio of…