Related papers: Monotone Erasure Codes
Random Linear Network Coding (RLNC) provides a theoretically efficient method for coding. Some of its practical drawbacks are the complexity of decoding and the overhead due to the coding vectors. For computationally weak and battery-driven…
Recently, network error correction coding (NEC) has been studied extensively. Several bounds in classical coding theory have been extended to network error correction coding, especially the Singleton bound. In this paper, following the…
Traditional machine learning algorithms use data from databases that are mutable, and therefore the data cannot be fully trusted. Also, the machine learning process is difficult to automate. This paper proposes building a trustable machine…
This paper investigates linear-time decoding algorithms for two classes of error-correcting codes. One of the classes is monotone codes which are known as single deletion codes. The other is azinv codes which are known as single balanced…
Hinging on ideas from physical-layer network coding, some promising proposals of coded random access systems seek to improve system performance (while preserving low complexity) by means of packet repetitions and decoding of linear…
This work investigates the fundamental limits of communication over a noisy discrete memoryless channel that wears out, in the sense of signal-dependent catastrophic failure. In particular, we consider a channel that starts as a memoryless…
Blockchain technology has emerged as a revolutionary tool in ensuring data integrity and security in digital transactions. However, the current approaches to data verification in blockchain systems, particularly in Ethereum, face challenges…
The question whether RM codes are capacity-achieving is a long-standing open problem in coding theory that was recently answered in the affirmative for transmission over erasure channels [1], [2]. Remarkably, the proof does not rely on…
Linear codes have diverse applications in secret sharing schemes, secure two-party computation, association schemes, strongly regular graphs, authentication codes and communication. There are a large number of linear codes with few weights…
The problem of finding code distance has been long studied for the generic ensembles of linear codes and led to several algorithms that substantially reduce exponential complexity of this task. However, no asymptotic complexity bounds are…
Motivated by average-case trace reconstruction and coding for portable DNA-based storage systems, we initiate the study of \emph{coded trace reconstruction}, the design and analysis of high-rate efficiently encodable codes that can be…
Large-scale systems with all-flash arrays have become increasingly common in many computing segments. To make such systems resilient, we can adopt erasure coding such as Reed-Solomon (RS) code as an alternative to replication because…
Blockchain is a type of decentralized distributed network which acts as an immutable digital ledger. Despite the absence of any central governing authority to validate the blocks in the ledger, it is considered secure and immutable due to…
Blockchains have recently been under the spotlight due to the boom of cryptocurrencies and decentralized applications. There is an increasing demand for querying the data stored in a blockchain database. To ensure query integrity, the user…
In this paper we consider the variable-length lossless source coding for discrete memoryless sources. We proposes a new encryption framework for securely transmitting codewords over a noiseless channel. The proposed source encryption…
Blockchain is a distributed ledger with wide applications. Due to the increasing storage requirement for blockchains, the computation can be afforded by only a few miners. Sharding has been proposed to scale blockchains so that storage and…
Storing big data directly on a blockchain poses a substantial burden due to the need to maintain a consistent ledger across all nodes. Numerous studies in decentralized storage systems have been conducted to tackle this particular…
Consider two remote nodes (encoder and decoder), each with a binary sequence. The encoder's sequence $X$ differs from the decoder's sequence $Y$ by a small number of edits (deletions and insertions). The goal is to construct a message $M$,…
This article considers the performance of digital communication systems transmitting messages over finite-state erasure channels with memory. Information bits are protected from channel erasures using error-correcting codes; successful…
Machine learning algorithms learn from data and use data from databases that are mutable; therefore, the data and the results of machine learning cannot be fully trusted. Also, the machine learning process is often difficult to automate. A…