Related papers: Coding schemes for locally balanced constraints
We consider decoding of binary Tanner codes using message-passing iterative decoding and linear programming (LP) decoding in MBIOS channels. We present new certificates that are based on a combinatorial characterization for local-optimality…
This paper addresses the problem of learning binary hash codes for large scale image search by proposing a novel hashing method based on deep neural network. The advantage of our deep model over previous deep model used in hashing is that…
Visual localization algorithms have achieved significant improvements in performance thanks to recent advances in camera technology and vision-based techniques. However, there remains one critical caveat: all current approaches that are…
Iterative bit flipping decoders are an efficient and effective decoder choice for decoding codes which admit a sparse parity-check matrix. Among these, sparse $(v,w)$-regular codes, which include LDPC and MDPC codes are of particular…
Composite DNA is a recent method to increase the base alphabet size in DNA-based data storage.This paper models synthesizing and sequencing of composite DNA and introduces coding techniques to correct substitutions, losses of entire…
DNA as a data storage medium has several advantages, including far greater data density compared to electronic media. We propose that schemes for data storage in the DNA of living organisms may benefit from studying the reconstruction…
It was shown in \cite{GXY18} that the length $n$ of a $q$-ary linear locally recoverable code with distance $d\ge 5$ is upper bounded by $O(dq^3)$. Thus, it is a challenging problem to construct $q$-ary locally recoverable codes with…
This paper deals with two related problems, namely distance-preserving binary embeddings and quantization for compressed sensing . First, we propose fast methods to replace points from a subset $\mathcal{X} \subset \mathbb{R}^n$, associated…
This paper explores the design of convolutional codes for varying constraint lengths, focusing on their role in error correction in digital communication systems. Convolutional codes are essential in achieving reliable data transmission…
We consider the problem of joint source and channel coding of structured data such as natural language over a noisy channel. The typical approach to this problem in both theory and practice involves performing source coding to first…
A locally recoverable code of locality $r$ over $\mathbb{F}_{q}$ is a code where every coordinate of a codeword can be recovered using the values of at most $r$ other coordinates of that codeword. Locally recoverable codes are efficient at…
Binary constant weight codes have important applications and have been studied for many years. Optimal or near-optimal binary constant weight codes of small lengths have been determined. In this paper we propose a new construction of…
Locally Decodable Codes (LDCs) are error correcting codes that admit efficient decoding of individual message symbols without decoding the entire message. Unfortunately, known LDC constructions offer a sub-optimal trade-off between rate,…
In the trace reconstruction problem, one seeks to reconstruct a binary string $s$ from a collection of traces, each of which is obtained by passing $s$ through a deletion channel. It is known that $\exp(\tilde O(n^{1/5}))$ traces suffice to…
A binary code is said to be a disjunctive list-decoding $s_L$-code (LD $s_L$-code), $s \ge 2$, $L \ge 1$, if the code is identified by the incidence matrix of a family of finite sets in which the union (or disjunctive sum) of any $s$ sets…
The study of constant-weight codes in $\ell_1$-metric was motivated by the duplication-correcting problem for data storage in live DNA. It is interesting to determine the maximum size of a code given the length $n$, weight $w$, minimum…
Pseudo-Boolean constraints are omnipresent in practical applications, and thus a significant effort has been devoted to the development of good SAT encoding techniques for them. Some of these encodings first construct a Binary Decision…
We give the first polynomial-time algorithm for robust regression in the list-decodable setting where an adversary can corrupt a greater than $1/2$ fraction of examples. For any $\alpha < 1$, our algorithm takes as input a sample…
The goal of this paper is to set a constraint programming framework to solve lot-sizing problems. More specifically, we consider a single-item lot-sizing problem with time-varying lower and upper bounds for production and inventory. The…
Deepening and widening convolutional neural networks (CNNs) significantly increases the number of trainable weight parameters by adding more convolutional layers and feature maps per layer, respectively. By imposing inter- and intra-group…