相关论文: Error Correcting Index Codes and Matroids
We consider the problem of coding over the multi-user Interference Channel (IC). It is well-known that aligning the interfering signals results in improved achievable rates in certain setups involving more than two users. We argue that in…
Permutation codes were extensively studied in order to correct different types of errors for the applications on power line communication and rank modulation for flash memory. In this paper, we introduce the neural network decoders for…
Given two matroids $\mathcal{M}_1$ and $\mathcal{M}_2$ over the same ground set, the matroid intersection problem is to find the maximum cardinality common independent set. In the weighted version of the problem, the goal is to find a…
Perturbed graphic matroids are binary matroids that can be obtained from a graphic matroid by adding a noise of small rank. More precisely, r-rank perturbed graphic matroid M is a binary matroid that can be represented in the form I +P,…
An $(m,n,a,b)$-tensor code consists of $m\times n$ matrices whose columns satisfy `$a$' parity checks and rows satisfy `$b$' parity checks (i.e., a tensor code is the tensor product of a column code and row code). Tensor codes are useful in…
Network coding is a new technique to transmit data through a network by letting the intermediate nodes combine the packets they receive. Given a network, the network coding solvability problem decides whether all the packets requested by…
The growing demand for highly reliable communication systems drives the research and development of algorithms that identify and correct errors during data transmission and storage. This need becomes even more critical in hard-to-access or…
The correspondence between linear codes and representable matroids is well known. But a similar correspondence between quantum codes and matroids is not known. We show that representable symplectic matroids over a finite field…
This paper considers the problem of code design for a channel where communications and radar systems coexist, modeled as having both Additive White Gaussian Noise (AWGN) and Additive Radar Interference (ARI). The issue of how to adapt or…
It is well known that the minimum distance for linear network codes plays the same role as the minimum distance for classical error control codes. However, Yang and Yeung (2008) discovered that for nonlinear network codes, the minimum…
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…
Assume that a graph $G$ models a detection system for a facility with a possible ``intruder," or a multiprocessor network with a possible malfunctioning processor. We consider the problem of placing detectors at a subset of vertices in $G$…
Quantum metrology has been making amazing progress in the past decades. It is always in researchers' interest to search for new optimal states that improve parameter estimation. In this paper, we point out a connection between the code's…
The problem of stabilizing an unstable plant over a noisy communication link is an increasingly important one that arises in applications of networked control systems. Although the work of Schulman and Sahai over the past two decades, and…
The rotation of trapped molecules offers a promising platform for quantum technologies and quantum information processing. In parallel, quantum error correction codes that can protect quantum information encoded in rotational states of a…
For a simple model of mutually interacting qubits it is shown how the errors induced by mutual interactions can be eliminated using concatenated coding. The model is solved exactly for arbitrary interaction strength, for two well-known…
We consider the decoding of rank metric codes assuming the error matrix is symmetric. We prove two results. First, for rates $<1/2$ there exists a broad family of rank metric codes for which any symmetric error pattern, even of maximal rank…
Multiclass learning problems involve finding a definition for an unknown function f(x) whose range is a discrete set containing k > 2 values (i.e., k ``classes''). The definition is acquired by studying collections of training examples of…
In this paper, we shed light on how an adaptive, efficient error coding in the transport layer helps ensure the application requirements. We recap the use of MDS codes and show that binary coding can significantly reduce the complexity and…
We develop an approach through geometric functional analysis to error correcting codes and to reconstruction of signals from few linear measurements. An error correcting code encodes an n-letter word x into an m-letter word y in such a way…