Related papers: Block Circulant Codes with Application to Decentra…
Recently, rate-1/n zero-terminated (ZT) and tail-biting (TB) convolutional codes (CCs) with cyclic redundancy check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short blocklengths.…
In large scale distributed storage systems (DSS) deployed in cloud computing, correlated failures resulting in simultaneous failure (or, unavailability) of blocks of nodes are common. In such scenarios, the stored data or a content of a…
Construction of high rate Space Time Block Codes (STBCs) with low decoding complexity has been studied widely using techniques such as sphere decoding and non Maximum-Likelihood (ML) decoders such as the QR decomposition decoder with M…
A code over a finite alphabet is called locally recoverable (LRC) if every symbol in the encoding is a function of a small number (at most $r$) other symbols. We present a family of LRC codes that attain the maximum possible value of the…
This paper proposes a novel maximum-likelihood (ML) soft-decision decoding framework for linear block codes, termed error-building decoding (EBD). The complete decoding process can be performed using only the parity-check matrix, without…
Spatially-Coupled (SC)-LDPC codes are known to have outstanding error-correction performance and low decoding latency. Whereas previous works on LDPC and SC-LDPC codes mostly take either an asymptotic or a finite-length design approach, in…
Blockchains offer a useful abstraction: a trustworthy, decentralized log of totally ordered transactions. Traditional blockchains have problems with scalability and efficiency, preventing their use for many applications. These limitations…
We consider linear cyclic codes with the locality property, or locally recoverable codes (LRC codes). A family of LRC codes that generalizes the classical construction of Reed-Solomon codes was constructed in a recent paper by I. Tamo and…
A linear block code with dimension $k$, length $n$, and minimum distance $d$ is called a locally repairable code (LRC) with locality $r$ if it can retrieve any coded symbol by at most $r$ other coded symbols. LRCs have been recently…
Decentralized crypto-currencies based on the blockchain architecture under-utilize available network bandwidth, making them unable to scale to thousands of transactions per second. We define the Blockclique architecture, that addresses this…
Bitcoin is the first successful decentralized global digital cash system. Its mining process requires intense computational resources, therefore its usefulness remains a disputable topic. We aim to solve three problems with Bitcoin and…
We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First,…
An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be…
Petabyte-scale distributed storage systems are currently transitioning to erasure codes to achieve higher storage efficiency. Classical codes like Reed-Solomon are highly sub-optimal for distributed environments due to their high overhead…
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
A locally decodable code (LDC) C:{0,1}^k -> {0,1}^n is an error correcting code wherein individual bits of the message can be recovered by only querying a few bits of a noisy codeword. LDCs found a myriad of applications both in theory and…
Purposely modular, this protocol enables customization of several protocol properties, including the consensus properties implemented, blockchain type, the roots used, and virtual machine opcodes, among others. These modules enable…
From currency to cloud storage systems, the continuous rise of the blockchain technology is moving various information systems towards decentralization. Blockchain-based decentralized storage networks (DSNs) offer significantly higher…
We introduce a construction for protocols for fault-tolerant quantum computing based on code concatenation and transversal gates. These protocols can be interpreted as families of quantum circuits of low-weight stabilizer measurements…
Although blockchain, the supporting technology of Bitcoin and various cryptocurrencies, has offered a potentially effective framework for numerous applications, it still suffers from the adverse affects of the impossibility triangle.…