Related papers: On Minimum Distances for Error Correction and Dete…
This note presents some new information on how the minimum distance of the generalized toric code corresponding to a fixed set of integer lattice points S in R^2 varies with the base field. The main results show that in some cases, over…
Motivated by applications to DNA storage, we study reconstruction and list-reconstruction schemes for integer vectors that suffer from limited-magnitude errors. We characterize the asymptotic size of the intersection of error balls in…
In this paper we show the usability of the Gray code with constant weight words for computing linear combinations of codewords. This can lead to a big improvement of the computation time for finding the minimum distance of a code. We have…
Quantifying the differences between networks is a challenging and ever-present problem in network science. In recent years a multitude of diverse, ad hoc solutions to this problem have been introduced. Here we propose that simple and…
We investigate random feature models in which neural networks sampled from a prescribed initialization ensemble are frozen and used as random features, with only the readout weights optimized. Adopting a statistical-physics viewpoint, we…
The surface code is a powerful quantum error correcting code that can be defined on a 2-D square lattice of qubits with only nearest neighbor interactions. Syndrome and data qubits form a checkerboard pattern. Information about errors is…
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…
Consider an ensemble of regular generalized LDPC (GLDPC) codes and assume that the same component code is associated with each parity check node. To decode a GLDPC code from the ensemble, we use the bit flipping bounded distance decoding…
This paper considers the problem of securing a linear network coding system against an adversary that is both an eavesdropper and a jammer. The network is assumed to transport n packets from source to each receiver, and the adversary is…
We introduce the concept of an \ff-maximal error-detecting block code, for some parameter \ff{} between 0 and 1, in order to formalize the situation where a block code is close to maximal with respect to being error-detecting. Our…
New bounds on classification error rates for the error-correcting output code (ECOC) approach in machine learning are presented. These bounds have exponential decay complexity with respect to codeword length and theoretically validate the…
We propose an algebraic setup for end-to-end physical-layer network coding based on submodule transmission. We introduce a distance function between modules, describe how it relates to information loss and errors, and show how to compute…
The Graph Edit Distance (GED) is an important metric for measuring the similarity between two (labeled) graphs. It is defined as the minimum cost required to convert one graph into another through a series of (elementary) edit operations.…
There have been extensive studies on solving differential equations using physics-informed neural networks. While this method has proven advantageous in many cases, a major criticism lies in its lack of analytical error bounds. Therefore,…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
Generalization error bounds are essential to understanding machine learning algorithms. This paper presents novel expected generalization error upper bounds based on the average joint distribution between the output hypothesis and each…
Rate-compatible error-correcting codes (ECCs), which consist of a set of extended codes, are of practical interest in both wireless communications and data storage. In this work, we first study the lower bounds for rate-compatible ECCs,…
When digital data are transmitted over a noisy channel, it is important to have a mechanism allowing recovery against a limited number of errors. Normally, a user string of 0's and 1's, called bits, is encoded by adding a number of…
We define the error exponent of the typical random code as the long-block limit of the negative normalized expectation of the logarithm of the error probability of the random code, as opposed to the traditional random coding error exponent,…
We present a simple deterministic gap-preserving reduction from SAT to the Minimum Distance of Code Problem over $\F_2$. We also show how to extend the reduction to work over any finite field. Previously a randomized reduction was known due…