Related papers: Guess & Check Codes for Deletions and Synchronizat…

The explosion of the amount of data stored in cloud systems calls for more efficient paradigms for redundancy. While replication is widely used to ensure data availability, erasure correcting codes provide a much better trade-off between…

Consider an assignment of bits to the vertices of a connected graph $G(V,E)$ with the property that the value of each vertex is a function of the values of its neighbors. A collection of such assignments is called a {\em storage code} of…

We introduce Decision Tree Decoders (DTDs), which rely only on the sparsity of the binary check matrix, making them broadly applicable for decoding any quantum low-density parity-check (qLDPC) code and fault-tolerant quantum circuits. DTDs…

Recently, codes for correcting a burst of errors have attracted significant attention. One of the most important reasons is that bursts of errors occur in certain emerging techniques, such as DNA storage. In this paper, we investigate a…

We consider deletion correcting codes over a q-ary alphabet. It is well known that any code capable of correcting s deletions can also correct any combination of s total insertions and deletions. To obtain asymptotic upper bounds on code…

Data storage in Distributed Storage Systems (DSSs) is a multidimensional optimization problem. Using network coding, one wants to provide reliability, scalability, security, reduced storage overhead, reduced bandwidth for repair and minimal…

In this work, we derive upper bounds on the cardinality of tandem duplication and palindromic deletion correcting codes by deriving the generalized sphere packing bound for these error types. We first prove that an upper bound for tandem…

Distributed implementations are crucial in speeding up large scale machine learning applications. Distributed gradient descent (GD) is widely employed to parallelize the learning task by distributing the dataset across multiple workers. A…

The design of low-density parity-check (LDPC) code ensembles optimized for a finite number of decoder iterations is investigated. Our approach employs EXIT chart analysis and differential evolution to design such ensembles for the binary…

We study the application of polar codes in deletion channels by analyzing the cascade of a binary erasure channel (BEC) and a deletion channel. We show how polar codes can be used effectively on a BEC with a single deletion, and propose a…

In this paper, we analyze the tradeoff between coding rate and asymptotic performance of a class of generalized low-density parity-check (GLDPC) codes constructed by including a certain fraction of generalized constraint (GC) nodes in the…

The performance of Reed--Solomon codes (RS codes, for short) in the presence of insertion and deletion errors has attracted growing attention in recent literature. In this work, we further study this intriguing mathematical problem,…

An edit refers to a single insertion, deletion, or substitution. This paper aims to construct binary codes that can correct two edits. To do this, a necessary and sufficient condition for a code to be two-edit correctable is provided,…

We propose in this paper to exploit convolutional low density generator matrix (LDGM) codes for transmission of Bernoulli sources over binary-input output-symmetric (BIOS) channels. To this end, we present a new framework to prove the…

In distributed computing, slower nodes (stragglers) usually become a bottleneck. Gradient Coding (GC), introduced by Tandon et al., is an efficient technique that uses principles of error-correcting codes to distribute gradient computation…

Scientific computing workflows generate enormous distributed data that is short-lived, yet critical for job completion time. This class of data is called intermediate data. A common way to achieve high data availability is to replicate…

In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and…

Code retrieval is to find the code snippet from a large corpus of source code repositories that highly matches the query of natural language description. Recent work mainly uses natural language processing techniques to process both query…

With the use of belief propagation (BP) decoding algorithm, low-density parity-check (LDPC) codes can achieve near-Shannon limit performance. In order to evaluate the error performance of LDPC codes, simulators running on CPUs are commonly…

This paper investigates decoding of binary linear block codes over the binary erasure channel (BEC). Of the current iterative decoding algorithms on this channel, we review the Recovery Algorithm and the Guess Algorithm. We then present a…