Related papers: Block Circulant Codes with Application to Decentra…
In this paper we address the problem of decoding linearized Reed-Solomon (LRS) codes beyond their unique decoding radius. We analyze the complexity in order to evaluate if the considered problem is of cryptographic relevance, i.e., can be…
We revisit computationally relaxed locally decodable codes (crLDCs) (Blocki et al., Trans. Inf. Theory '21) and give two new constructions. Our first construction is a Hamming crLDC that is conceptually simpler than prior constructions,…
The distance profiles of linear block codes can be employed to design variational coding scheme for encoding message with variational length and getting lower decoding error probability by large minimum Hamming distance. %, e.g. the design…
Circular-shift linear network coding (LNC) is a class of vector LNC with local encoding kernels selected from cyclic permutation matrices, so that it has low coding complexities. However, it is insufficient to exactly achieve the capacity…
In a distributed space-time coding scheme, based on the relay channel model, the relay nodes co-operate to linearly process the transmitted signal from the source and forward them to the destination such that the signal at the destination…
The interoperability across multiple or many blockchains would play a critical role in the forthcoming blockchain-based data management paradigm. In particular, how to ensure the ACID properties of those transactions across an arbitrary…
Public blockchains have spurred the growing popularity of decentralized transactions and smart contracts, but they exhibit limitations on the transaction throughput, storage, and computation. To avoid transaction gridlock, public…
Cyclic codes are an interesting type of linear codes and have wide applications in communication and storage systems due to their efficient encoding and decoding algorithms. Inspired by the recent work on binary cyclic codes published in…
Since the creation of Bitcoin 15 years ago, there has been an explosion in the number of permissionless blockchains. Each of these blockchains provides an open ledger that anyone can read from and write to. In this multi-chain world, an…
Coded blockchains have acquired prominence as a promising solution to reduce storage costs and facilitate scalability. Within this class, Luby Transform (LT) coded blockchains are an appealing choice for scalability owing to the…
The surface code is the most studied error-correcting code thanks to its high threshold, simple decoding, and locality in two dimensions (2D). A key component of any code is its encoding circuit, which maps an unencoded state to the…
Discrete Laplacian operators arise ubiquitously in scientific computing and frequently appear in quantum algorithms for tasks such as linear algebra, Hamiltonian simulation, and partial differential equations. Block encoding provides the…
Locally repairable codes (LRCs) are a class of codes designed for the local correction of erasures. They have received considerable attention in recent years due to their applications in distributed storage. Most existing results on LRCs do…
Distributed storage systems for large-scale applications typically use replication for reliability. Recently, erasure codes were used to reduce the large storage overhead, while increasing data reliability. A main limitation of…
This paper reviews and highlights how coding schemes have been used to solve various problems in blockchain systems. Specifically, these problems relate to scaling blockchains in terms of their data storage, computation and communication…
We consider the locality of encoding and decoding operations in distributed storage systems (DSS), and propose a new class of codes, called locally encodable and decodable codes (LEDC), that provides a higher degree of operational locality…
An $[n,k]$ code $\mathcal{C}$ is said to be locally recoverable in the presence of a single erasure, and with locality parameter $r$, if each of the $n$ code symbols of $\mathcal{C}$ can be recovered by accessing at most $r$ other code…
LT (Luby transform) codes are a celebrated family of rateless erasure codes (RECs). Most of existing LT codes were designed for applications in which a centralized encoder possesses all message blocks and is solely responsible for encoding…
Constant-rate low-density parity-check (LDPC) codes are promising candidates for constructing efficient fault-tolerant quantum memories. However, if physical gates are subject to geometric-locality constraints, it becomes challenging to…
Locally decodable codes (LDCs) are error-correcting codes $C : \Sigma^k \to \Sigma^n$ that admit a local decoding algorithm that recovers each individual bit of the message by querying only a few bits from a noisy codeword. An important…